Place the chestnuts and 1/2 cup water in a small heatproof bowl. Microwave until the water is hot and the chestnuts have softened, about 3 minutes. Drain the chestnuts (reserving the liquid) and place in the bowl of a food processor. Blend with 1 tablespoon of the reserved liquid until finely ground. Add the 1 1/2 cups of the Parmesan, the ricotta and a large pinch of salt and pepper. Blend until completely smooth. Taste for seasoning and adjust with additional salt and pepper if needed. Add 1 egg and blend until well combined. Transfer to a mixing bowl and reserve.
Bring a large stockpot of salted water to a boil (it should taste like sea water).
While the water is coming to a boil, form the raviolis. Whisk the remaining egg in a small bowl with 1/2 teaspoon water. Place 5 wonton skins on a lightly floured work surface. Brush the wonton skins with the egg wash. Place a leveled tablespoon of the chestnut filling in the center of each wonton skin. Place 5 more wonton skins directly on top. Use your fingers to gently press the skins together. Use a 2 1/2-inch round cookie or biscuit cutter lightly dipped in flour to cut around the filling. Transfer the filled raviolis to a baking sheet lined with parchment paper and cover with a slightly damp paper towel. Make 15 additional raviolis with the remaining wonton skins and filling.
Once all of the raviolis are made, make the brown butter sauce. Place the butter, garlic and thyme in a large, straight-sided saute pan. Heat over medium heat until the butter starts to bubble and foam, about 5 minutes, stirring occasionally. Continue cooking until the foam subsides and brown specks start to appear, 1 to 2 minutes, stirring constantly. Turn off the heat and cover with a lid to keep warm while you cook the raviolis.
In batches, add the raviolis one at a time to the boiling water, stirring after every addition. Cook until the raviolis float to the top, about 2 minutes. Use a slotted spoon to remove from the water and add to the browned butter; it is okay if some pasta water gets in the sauce. Toss the raviolis in the sauce. Continue with the remaining raviolis.
To serve, remove the thyme sprigs and garlic from the sauce, reserving the thyme. Divide the raviolis and sauce among 4 plates. Sprinkle with the remaining cheese and crispy thyme leaves. If desired, lightly drizzle with balsamic vinegar. Use a peeler to thinly shave whole chestnuts over the entire dish.