Mix all the sauce ingredients in a separate bowl and set aside.
Heat 1 tablespoon of oil and 1 tablespoon of butter in a large skillet or wok over medium-high heat. Add the carrot and peppers, stir-frying until crisp-tender. Transfer the vegetables to a plate.
Increase the heat to high, add 1 tablespoon of oil, and sear the beef for about 2 minutes per side until crispy. Add more oil if needed. Cook the beef in batches if the skillet is crowded.
Return the vegetables to the skillet, along with green onions. Pour in the sauce and mix well. Reduce heat to medium-low and simmer until the sauce thickens, about 3 minutes.
Garnish with sesame seeds if desired and serve hot.
Notes
Notes: For a spicier kick, adjust the Sriracha to suit your taste.