Step 1

Arrange a rack in the middle of the oven and heat the oven to 450°F. Meanwhile, trim the stem ends from 1 1/2 pounds Brussels sprouts. Halve the sprouts through the stem or quarter if large. Peel and discard any loose leaves if they are yellowed or darker in spots.

Step 2

Transfer the Brussels sprouts to a large bowl. Add 3 tablespoons olive oil, 1 teaspoon kosher salt, and 1/4 teaspoon of the coarsely ground black pepper. Toss to coat. Transfer to a rimmed baking sheet and arrange cut-side down in a single layer with a little bit of space in between the sprouts.

Step 3

Roast for 12 minutes. Toss and spread back into an even layer. Roast until the leaves are dark brown and crisp and the cut-sides of the sprouts are browned, 6 to 13 minutes more. Meanwhile, prepare the sauce.

Step 4

Finely grate 1 ounce Pecorino Romano cheese and 1 ounce Parmesan cheese (about 1/2 cup each), or measure out 1/3 cup store-bought grated each. Place both in a small saucepan. Add the remaining 1 teaspoon coarsely ground black pepper, 1/2 cup whole milk, and 2 teaspoons cornstarch.

Step 5

Cook over low heat, whisking constantly, until melted, bubbly, and thickened, 5 to 10 minutes total. (It will look thin and grainy at first, but will thicken and come together after heating.) Remove the saucepan from the heat and cover to keep warm.

Step 6

Transfer the Brussels sprouts to a serving platter. Drizzle with the sauce. Serve with more grated Parmesan or Pecorino cheese and coarsely ground black pepper.