Put the ricotta, eggs, Parmigiano and nutmeg in a medium bowl, season with salt and pepper and fold together with a rubber spatula until just incorporated. Spoon the ricotta mixture into a piping bag fitted with a number 3/8 inch plain tip and refrigerate for at least 1 hour, but no more than 8 hours.

Line a baking sheets with parchment paper and lightly dust it with rice flour.

Lay pasta sheets on a floured surface and use a wheel cutter or sharp chef’s knife to cut them into 48 3-inch squares (using a ruler as a guide is helpful). Lay half of the squares on the floured surface and keep the others under a damp kitchen towel. Pipe about 1 ½ tablespoons of filling into the center of half the squares. Use a pastry brush or your finger to brush the edges of the squares with water, then place one of the remaining squares on top of each one, using your fingers to press any air out. Tightly seal the edges, then trim the edges with the wheel cutter and arrange the tortelli on the rice-flour-dusted baking sheet.

The tortelli can be refrigerated for up to 1 day or frozen for up to 2 months.

When ready to cook, fill a large pot about two-thirds full with water, salt it liberally, and bring to a boil over high heat.

Meanwhile, melt the butter in a medium sauté pan over medium-high heat. Add the sage leaves and cook, stirring with a wooden spoon, until the butter is browned and fragrant, about 2 minutes. Remove from heat and cover to keep warm.

When the water has come to a boil, lower the heat slightly to a gentle boil and gingerly add the tortelli a few at a time. Stir carefully once to keep them from sticking together, then cook until he tortelli float to the surface, 2 to 3 minutes for fresh, 4 to 5 minutes for frozen. Remove with a slotted spoon, letting the excess water run off, and transfer to a bowl.

Add the tortelli to the sage butter and toss briefly to coat. Divide among individual plates, sprinkle each serving with Parmigiano, and serve immediately.

Pour the oil into a wide heavy sauté pan and heat over medium-high heat until the oil is shimmering and almost smoking. Add the onions and garlic and cook, stirring with a wooden spoon, until softened but not browned, about 4 minutes. Add the mushrooms, season with salt and a few grinds of black pepper, and cook, stirring, until the begin to give off their liquid, about 5 minutes, adding more oil if the pan becomes too dry.

Stir in the tomato paste, stirring to coat the mushrooms, and cook until it turns a shade darker, about, about 2 minutes. Stir in the rosemary, sage, and red pepper flakes.

Pour in the wine, bring to a simmer, and simmer until it has evaporated, about 5 minutes. Stir in the stock and bring it to a simmer, then lower the heat, partially cover the pan, and let simmer, stirring occasionally, until the sauce is thick enough to coat the back of a wooden spoon, about 1 hour. The sauce can be cooled and refrigerated in an airtight container for up to 3 days; reheat gently before proceeding.

Meanwhile, about 20 minutes before the sauce is ready, fill a large pot 2/3 full with water and salt it liberally. Bring to a boil over high heat. Add the pasta and cook until al dente, about 4 minutes for fresh, or 9 minutes for dried. Drain the pasta and add it to the sauce. Toss well.

Divide pasta and sauce among plates, layering pasta pieces with mushrooms and sauce. Shave some cheese over top and a few more grinds of black pepper.