With the rack in the middle position, preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
On the prepared baking sheet, combine the onion, squash and oil. Season with salt and pepper. Bake for about 45 minutes, stirring occasionally, or until tender and lightly browned.
In a food processor, purée the vegetables, Parmesan, bread crumbs and nutmeg until smooth. Season with salt and pepper. Refrigerate the filling for 1 hour or until completely chilled.
On a lightly floured surface, divide the pasta dough into 4 pieces and shape into rectangles. With a pasta machine, run 1 piece of dough at a time through the rollers. Do not over flour; the dough should be slightly sticky. Continue running the dough through the machine, gradually narrowing the gap between the rollers, until setting 5. Place the dough on a lightly floured surface.
Spoon the squash filling into a pastry bag fitted with a ½-inch (1 cm) plain tip. Pipe 2 straight bands of filling the length of the dough, ½ inch (1 cm) from the top and bottom edges of the dough. Fold the pasta edges over the filling. Fold over a second time, leaving about ¾ inch (2 cm) between each band of filling. Dust the underside of the pasta with flour. With the handle of a wooden spoon, firmly press and seal the bands at ¾-inch (1.5 cm) intervals. Each sealed joint should be about ½ inch (1 cm) wide.
With a pasta wheel cutter or a knife, cut between the 2 bands of filling and between each agnolotto. Place them on a lightly floured baking sheet. Avoid overlapping and do not cover. Refrigerate while preparing the sauce, or freeze at this stage, if desired.
Meanwhile, in a saucepan over medium heat, soften the shallots in 2 tbsp of the butter. Deglaze with the wine and simmer for 5 minutes. Add the broth, porcini mushrooms and Parmesan rind. Bring to a boil and let the sauce reduce to 1 cup (250 ml), about 20 minutes. Remove the rind. Season with salt and pepper. Set aside.
In a large pot of salted boiling water, cook the agnolotti for 4 to 6 minutes or until tender. Drain.
Add the agnolotti and the remaining butter (¼ cup/55 g) to the sauce. Gently stir to coat. Adjust the seasoning.