Step 1

Preheat oven to 450°F. Toss together Brussels sprouts, oil, pepper, and 1 teaspoon of the salt. Arrange in a single layer on a rimmed baking sheet lined with aluminum foil. Roast in preheated oven until lightly browned, about 15 minutes. Remove from oven; reduce oven temperature to 425°F.

Step 2

While sprouts roast, whisk together flour and 1/2 cup of the milk in a bowl. Bring remaining 3 1/2 cups milk to a boil in a medium saucepan over medium-high. Whisk in flour mixture; cook, whisking occasionally, until slightly thickened, about 2 minutes. Whisk in cheeses and remaining 1 1/2 teaspoons salt. Remove from heat.

Step 3

Toss together roasted sprouts and crumbled bacon in a 2-quart square baking dish. Pour cheese mixture over sprouts-bacon mixture. Toss together panko, butter, and thyme in a bowl; sprinkle over mixture in baking dish. Bake at 425°F until lightly browned, 12 to 15 minutes.