Butternut Squash Parmesan Dip

Arrange a rack in the middle of the oven and heat to 400°F.

Rub each half of the squash, inside and out, with a teaspoon of olive oil and season with salt and pepper. Place cut-side down on a foil-lined baking sheet, with one sprig of thyme tucked into the cavity of each half. Roast until a fork poked into the non-hollow end of the squash slides in easily, about 45 minutes. Let it sit until the squash is cool enough to handle.

Scoop out the flesh of the squash halves and add to the bowl of a food processor. Add 3/4 cup of the cheese, the leaves from the remaining thyme sprig, nutmeg, and salt. Pulse until blended, then pour in the milk while the machine is running.

Transfer mixture to a small 8-inch baking dish or a shallow pie plate. Sprinkle on the remaining Parmesan and return to the oven for 15 minutes.

Set the oven to broil, and continue cooking until lightly browned on top, 2 to 3 minutes more.