“MY INSPIRATION comes from local ingredients,” said Charleston, S.C.-based chef Mike Lata. “But to be honest I’m a bit of a Europhile.” Since moving to the state’s Low Country 17 years ago, Mr. Lata has used the region’s outstanding produce and fresh fish the best way he knows how: by applying the classical technique he learned in kitchens around the U.S. and in France.

In this recipe for coddled eggs topped with sautéed chanterelle mushrooms, crab meat and croutons—Mr. Lata’s second Slow Food Fast contribution—he lines...