Heat 1/4 cup olive oil in a 5-quart saute pan with high sides over medium heat. Add bacon and cook until crisp, about 8 minutes. Add shallots, half the mushrooms, 1/8 teaspoon salt, and a pinch of pepper and cook until wilted and nicely browned, about 5 minutes. Remove and set aside. Add another 1/4 cup olive oil, remaining mushrooms, 1/8 teaspoon salt, and a pinch of pepper and repeat with remaining mushrooms.

Add remaining tablespoon olive oil and butter to pan and heat over medium-high heat until butter has melted. Add brussels sprouts, 1/2 teaspoon salt, and 1/2 teaspoon pepper and cook until sprouts are lightly caramelized, 6 to 7 minutes. Add sauteed mushrooms, chicken stock, and remaining 1 teaspoon salt. Cook, stirring occasionally, until stock has evaporated by half. Cover pan, lower temperature to medium-low, and continue to cook until brussels sprouts are tender, 10 to 12 minutes.