Step 1

Preheat oven to 400°F. Toss together brussels sprouts, pearl onions, shallots, thyme, and 1/4 cup oil on a large rimmed baking sheet; sprinkle with pepper and 1 teaspoon salt. Roast in preheated oven until tender and browned, about 30 minutes. Remove from oven; remove and discard thyme sprigs.

Step 2

While brussels sprout mixture roasts, heat remaining 1/4 cup oil in a large skillet over medium-high. Add mushrooms; cook, stirring occasionally, until just starting to brown, 6 to 8 minutes. Reduce heat to medium-low; cook, stirring occasionally, until nicely browned and nearly crisp, 6 to 8 minutes. Remove from heat. Stir in soy sauce, smoked paprika, and remaining 1/2 teaspoon salt. Transfer mushrooms to paper towels to drain. Stir mushroom mixture into brussels sprout mixture just before serving.