Melt 1 tablespoon butter in a large skillet over medium heat; cook and stir garlic in hot butter until fragrant, 1 to 2 minutes. Stir broccoli and Brussels sprouts into garlic; add tomato and remaining 2 tablespoons butter. Season with salt and red pepper flakes.

Stir Brussels sprouts mixture until well combined, then cover the skillet and cook until browned on one side, about 5 minutes. Flip sprouts and broccoli, cover the skillet again, and cook until browned on the other side, about 4 minutes.