Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the bell peppers and 1/8 teaspoon each salt and pepper and cook, stirring, until crisp-tender, about 2 minutes. Transfer to a plate.
Heat the remaining tablespoon oil in the same skillet over medium-high heat. Add the chile flakes and cook 10 seconds, and then add the broccoli, 1/4 teaspoon each salt and pepper and 1/4 cup water. Cover and cook until the water evaporates and the broccoli is lightly browned and crisp-tender, about 4 minutes.
Toss in the peppers, peanuts and 1/8 teaspoon each salt and pepper and serve.