In a small bowl, whisk together soy sauce, BBQ sauce, maple syrup, minced garlic, ginger, sesame oil, and red pepper flakes until well combined. Set aside. While the sauce comes together, prepare all vegetables: slice zucchini into 1/4-inch thick rounds, halve or quarter mushrooms depending on size, and cut carrot into thin matchsticks. I find freshly minced garlic makes a noticeable difference in aroma and flavor, so don't skip that step. Have all ingredients ready before you start cooking, as stir-frying moves quickly.
Heat a large skillet or wok over medium-high heat and add the ground beef. Cook for 5-7 minutes, breaking it apart with a spoon as it cooks, until the beef is fully browned with no pink remaining. Transfer the cooked beef to a clean bowl and set aside. Don't rinse the pan—the flavorful browned bits stuck to the bottom (called fond) will add depth to the final dish.
In the same skillet, add the sliced zucchini, mushrooms, and carrot matchsticks. Cook over medium-high heat for 2-3 minutes, stirring occasionally, until the vegetables are tender but still have a slight crunch. I like to keep stir-fry vegetables slightly firm rather than soft—they'll continue cooking when the sauce is added, and the texture is much more satisfying.
Return the cooked ground beef to the skillet with the vegetables. Pour in the sauce mixture from Step 1 and stir everything together over medium-high heat for 2 minutes, ensuring the sauce coats all ingredients evenly and heats through. Taste and adjust seasoning with salt and pepper as needed. The sauce should glaze the beef and vegetables lightly, not pool at the bottom of the pan.
Transfer the stir-fry to a serving platter and garnish with chopped chives. Serve immediately over steamed rice, in lettuce cups for a lighter option, or over noodles. The dish is best enjoyed right after cooking while the flavors are vibrant and the vegetables still have their bite.