Heat 2 tablespoons oil in a large skillet or wok over medium-high heat. Add garlic, chile, broccoli and onion and cook, stirring often, until broccoli turns bright green. Transfer to a large bowl and add remaining tablespoon oil to skillet. When shimmering hot, shake excess marinade off of beef and add it to pan in a single layer. Brown well on both sides. Return broccoli mixture to skillet, add sauce, and cook, tossing frequently, until sauce thickens and broccoli is crisp-tender, about 2 minutes.