1/3cupmashed roasted winter squash (such as butternut)
1/4cupunsalted butter, (2 oz.)
2tablespoonsall purpose flour
1 - 2tablespoonsminced fresh sage
4oz.grated gruyere, divided
Place a rack in the center of the oven and preheat to 425º. Line a 12x18" baking sheet with parchment paper and place on top of another baking sheet (these tend to over-brown on their bottoms.)
Combine the milk, squash, butter, and salt in a medium saucepan over medium high heat. Bring to a boil, stirring occasionally. Dump in the flour and cook, stirring constantly, until the mixture forms a ball and a film forms on the bottom of the pan, a few minutes.
Dump the mixture in the bowl of a stand mixer fitted with the paddle. Beat on medium speed for a minute or so to release some heat, then add the eggs one at a time, beating until combined and smooth after each addition. Add in the sage and three quarters of the cheese, beating to combine. Scrape down the sides of the bowl and the paddle and fold a few times to make sure the mixture is homogenous.
Using a #40 spring-loaded ice cream scoop (or a piping bag fitted with a #8 plain tip, or the old spoon-and-finger method) scoop out 20 balls of the mixture and place them, 4x5, on the parchmented pan.
Bake until puffed and golden, about 25 minutes. Reduce the oven temperature to 350º and bake for an additional 10 minutes or so, to dry out the centers slightly. (If underbaked, the gougeres will deflate as they cool.)
These are best served warm from the oven, but will keep for a couple days at room temp. You can re-toast them before enjoying, if you like.
Nutritional values are based on one of twenty puffs.