How to Make It
Line a large rimmed baking sheet with wax paper. In a large bowl, blend the ricotta with the flour, Parmesan, egg yolks, 3/4 teaspoon of salt and 1/4 teaspoon of pepper. Spoon the gnocchi dough into a large, sturdy resealable plastic bag. Cut off a 1/2-inch corner from the bag. Pipe the dough onto the prepared baking sheet in five 1-foot-long strips about 3/4 inch wide. Cover with plastic wrap and freeze until firm, about 3 hours.
Meanwhile, in a small saucepan of boiling salted water, cook the corn until just tender, about 3 minutes. Drain and return the corn to the saucepan. Stir in 2 tablespoons of the butter.
In a very large skillet, heat 2 tablespoons of the olive oil until shimmering. Add the mushrooms, season with salt and pepper and cook over moderately high heat until browned on the bottom, about 5 minutes. Stir and cook until browned and tender, about 4 minutes longer. Transfer to a plate. Add the wine to the skillet and boil over moderately high heat until reduced by half, about 3 minutes. Add the chicken stock and boil until reduced to 3/4 cup, 4 minutes. Add the corn and set aside.
Preheat the oven to 275°. Let the gnocchi dough stand at room temperature for 5 minutes. Cut the strips into 1-inch lengths. Sprinkle with the cornstarch and toss gently to coat.
In a large nonstick skillet, heat 2 tablespoons of the oil. Add half of the gnocchi and cook over high heat until browned on the bottom, about 1 minute. Reduce the heat to moderately high. Using a spatula, turn the gnocchi and brown the other side, 1 to 2 minutes. Transfer to a baking sheet; keep warm in the oven. Repeat with the remaining 2 tablespoons of oil and the gnocchi.
Reheat the corn in the skillet. Add the mushrooms, tarragon and the remaining 2 tablespoons of butter and season with salt and pepper. Transfer the gnocchi to plates, spoon the mushroom ragout around them and serve.
Sheep's-milk ricotta is often blended with some cow's milk. It's available at specialty food stores and by mail order from Old Chatham Sheepherding Company (888-SHEEP-60 or blacksheepcheese.com). Alternatively, use cow's-milk ricotta and drain it overnight in a fine strainer in the refrigerator; discard the whey.