In a medium Dutch oven, or a large skillet, melt butter over medium heat. Cook until the foam subsides, the milk solids turn golden brown, and it smells nutty and toasty, about 3 to 4 minutes.

Stir in shallots and cook until slightly softened, about 2 minutes. Add squash, sage, a large pinch of salt, black pepper, and red-pepper flakes, and cook until squash is golden at the edges and begins to soften, 12 to 17 minutes.

Add stock and bring to a simmer. Stir in orzo, lemon zest, and 1 teaspoon salt. Cover the pan and simmer over medium-low heat until orzo is just tender and most of the liquid is absorbed, 14 to 18 minutes, stirring once or twice. If the pan dries out before the orzo and squash are tender, add a splash or two of water.

Remove pan from heat and stir in Parmesan. Taste and add more salt if needed, and a squeeze of lemon juice if the dish needs brightness. Dollop with ricotta if using, and sprinkle with more grated Parmesan and black pepper just before serving, garnishing the top with more red-pepper flakes and sage.