Winter Squash Gnocchi with Brown Butter and Sage

head of garlic, top third cut off

Extra-virgin olive oil, for rubbing

baking potatoes

butternut squash—peeled, seeded and cut into 2-inch pieces

large egg yolks, at room temperature

fresh ricotta cheese

minced flat-leaf parsley

Kosher salt

all-purpose flour, plus more for dusting

unsalted butter

sage leaves, thinly sliced

fresh thyme, finely chopped

Parmigiano-Reggiano shavings, for serving