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.
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.
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.
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.
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.
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.