A certain kind of eater’s pulse is quickened by unfamiliar, suggestive phrases like “peachleaf ice cream” and “garlic seeds,” phrases that mean little to most people. Colin and Renee Alevras, proprietors of the Tasting Room, are wagering that there are more than a few such eaters, and they seem to be right.

For six years, the couple operated the Tasting Room on East First Street, where Mr. Alevras’s inventive, exactingly fresh cooking shone brightly despite the comically small 25-seat space. Now the restaurant has relocated to a space on Elizabeth Street, gargantuan by comparison, with two attractive, homey dining rooms where the ambitious food can properly hold court. The kitchen has elbow room too, and newfangled luxuries like gas heat.

“Market-driven” is an overused term, but the local suppliers who almost solely constitute his market drive Mr. Alevras fast and relentlessly. When he has access to a good ingredient it’s all over the menu. One evening, five of 16 dishes starred mushrooms, including chanterelles served with a poached egg ($32), and caramelly roasted whole matsutakes, which, at an eye-widening $38 for a non-protein-based dish, tested (and rewarded) the dedication of the customer. A large chicken-of-the-woods mushroom ($28), cooked whole, had the startlingly convincing flavor of chicken, or at least chicken broth. With its smooth meatiness, the mushroom might pass for a bird if not for its gorgeous vermillion coloring. It received a chicken-like presentation, too, accompanied by buttery little potatoes and fresh green beans. A few days later, reddish, much drier bits of the same mushroom enriched the savor of a turbot entree ($32). Firm and tasty, the turbot was seasoned as well with those garlic seeds — actually berry-like embryonic cloves, with a buttery richness and mild roasted-garlic taste.

One of Mr. Alevras’s ways to give his food charisma is time-tested: lots of butter, olive oil, and salt. The second lies in careful shopping: He entrusts each dish’s deliciousness to the strength of its ingredients. Only occasionally is his trust misplaced, as it was in a shoulder of heritage Tamworth-breed pork ($26) whose thick-sliced meat, though superb and deeply sweet, needed something further to perk it up.

The third key to the food’s charisma can be found in the creativity and ephemerality of the preparations. Each Tasting Room meal might be your first and only chance to taste some of its novel items, and the menu descriptions, with their long lists of uncommon, pedigreed ingredients, drive that point home. Some of the taste-pairings are undeniable, but others are best approached with an open mind. A shallow serving of chilled pear soup ($9), given an herbal, vegetal tone by sorrel and lovage, had a milky consistency, a color of palest green, and a subtle taste. Nineteen of 20 chefs would find it too minimal and throw in a few shrimp or a squirt of truffle oil, but, accepted at face value, it was charming in its almost arbitrary simplicity.

Many appetizers are as substantial as the main courses. Three big blowfish tails ($14) — a meaty, dense seafood often euphemized as “sea squab” — were lightly breaded and complemented with shreds of cabbage and radishes in a thin creamy sauce; the dish had the spirit of a San Diego fish taco.A bright-pink terrine of guinea hen ($14) had a fantastic gamy taste, spiked with mustard and raw onion. And slices of lean, light-tasting lamb shoulder ($15), roasted rare and served cold, were coated in plenty of juicy olive oil, garlic, and fresh oregano, and further invigorated with a crumbling of rich goats’-milk feta.

The service isn’t up to speed yet. The menu requires a fair bit of explaining, and the staff seems ill-prepared to do so. The handcrafted nature of the dishes means too that there can be quite a wait for each one; the printed warning — “Let your server know about any postdinner plans” — should perhaps suggest instead to cancel them.

Desserts (all $9) aren’t quite up to the standard of the old Tasting Room. A peach cobbler was marvelously ripe but plain (that enticing peach-leaf ice cream on top resembled particularly fresh pistachio) and brioche bread pudding had very little going for it beyond butter.

Nearly all the restaurant’s wine, about 15 pages’ worth, comes from America, mostly from little, little-known wineries. It includes frequently changing by-the-glass choices in the $8–$12 zone, on up to a few vintages of Screaming Eagle, the cult cabernet that sounds like, and costs as much as, a motorcycle. Classic cocktails ($11) — a Collins, a Southside — are ennobled with fresh juices and fruits.

When the food is good, it’s breathtaking, but during the lulls one is sometimes reminded that these aren’t recipes with generations of tradition behind them. They’re thought up fresh by a single chef, inspired by the day’s ingredients, and the Alevrases’ gamble is that this one-man show can play on a larger stage. Thus far, the crowds thronging the new space seem satisfied that it can.

The Tasting Room, 264 Elizabeth St., between Houston and Prince streets, 212-358-7831.