Place the flour on a work surface and form a well. Add the yolks and salt, then mix with a fork until a rough dough forms. Knead until smooth and elastic, about 8 to 10 minutes. Wrap and chill for at least 30 minutes.
Melt the butter for the filling in a skillet over medium heat. Add the onion, sage, garlic, and mushrooms, and cook until golden and all liquid has evaporated, about 8–10 minutes. Cool slightly, then pulse in a food processor with mascarpone, truffle purée, Parmesan, salt, and pepper until smooth but not puréed. Chill if needed to firm.
Roll the dough through a pasta machine to 1–2 mm thickness. Lay one sheet on a floured surface and pipe or spoon small mounds (about 1 teaspoon each) of filling spaced 1 inch apart. Brush lightly with water, lay a second sheet over, press to seal and remove air, then cut into ravioli with a cutter or pasta wheel. Transfer to a floured tray and freeze until firm; store in an airtight container for up to 3 months.
Make the caramel butter by melting the sugar in a small saucepan until amber. Remove from heat, whisk in the butter, then the cream. Warm the porcini broth separately and keep both sauces warm.
Heat the oven to 400°F/200°C. Spread a thin, even layer of grated Parmesan on a parchment-lined baking sheet. Bake until golden and crisp, 5 to 7 minutes. Let cool, then break into shards.
Cook the ravioli in a large pot of boiling salted water until they float, about 2 minutes fresh or 3–4 minutes from frozen. Lift gently with a slotted spoon into a skillet with caramel butter and a splash of porcini broth. Toss to coat, adding broth as needed. Serve topped with crispy Parmesan.