For sauce, stir together the first four ingredients (through crushed red pepper).
Cut florets off broccoli stems and measure 2 cups florets. Peel stems and trim bottoms. Using a vegetable peeler, peel broccoli stems and carrots lengthwise into ribbons.
In a wok or very large skillet heat oil over medium-high heat. Add garlic; cook and stir 15 seconds. Add broccoli florets and ribbons, carrots, and green onions; cook and stir 4 to 5 minutes or until crisp-tender. Remove vegetables.
If necessary, add additional oil to wok. Add meat, half at a time; cook and stir 2 minutes or until slightly pink in center. Return cooked vegetables and remaining meat to wok; add sauce. Cook and stir until heated through. Sprinkle with peanuts.