Roast cubed butternut squash at 350°F (175°C) until very soft, then blend until smooth. If watery, strain through cheesecloth before using.
In a large bowl, add flour, squash purée, and spice. Mix together until combined. If sticky, add a little more flour. Knead briefly until you have a soft, smooth dough ball.
Roll dough into ½-inch ropes on a floured surface. Cut into bite-sized pieces with a bench scraper. Roll each piece over the back of a fork to make ridges. Place on a tray dusted with semolina.
Bring salted water to a boil. Add gnocchi and cook until they float, about 3 minutes. Reserve 1 cup pasta water.
In a skillet over medium heat, melt butter until lightly browned and nutty. Add sage leaves and prosciutto, cooking just ~30 seconds until fragrant.
Add cooked gnocchi straight to the pan with a splash of pasta water. Toss vigorously for ~15 seconds to coat.
Serve hot with grated Parmesan.
