Mushroom Ravioli with Oregano Brown-Butter Sauce

Pulse mushrooms in food processor until finely chopped. Heat oil in a 10-to 12-inch heavy skillet over medium-high heat until it shimmers. Add garlic and sauté until golden, about 1 minute. Add mushrooms, 1/2 teaspoon salt and 1/4 teaspoon pepper, and cover skillet. Cook mushrooms covered, 2 minutes, then uncover skillet and continue to cook mushrooms until all the liquid in the pan is evaporated, about 4 minutes. Remove from heat and stir in oregano. Let mushroom filling cool to room temperature.

Put 1 wonton wrapper on a lightly floured surface, keeping remaining wrappers in plastic wrap, and mound 1 teaspoon filling in center. Lightly brush edges of wrapper with water and fold wonton in half, pressing down around filling to force out air and seal edges well. Transfer ravioli to a dry kitchen towel. Make more ravioli with remaining wrappers and filling in same manner, transferring as formed to towel and turning occasionally to dry slightly.

Cook butter with oregano leaves, 1/4 teaspoon each of salt and pepper over moderate heat until butter begins to brown, about 3 minutes, and immediately remove from heat. Keep oregano butter warm, covered.

Cook ravioli in 2 batches in gently boiling salted water 6 minutes, or until they rise to surface and are tender (do not let water boil vigorously once ravioli have been added).

Carefully transfer ravioli with a slotted spoon (letting excess cooking liquid drip off) to 6 plates and top with oregano brown-butter sauce. Sprinkle each plate with some grated cheese.