In a small bowl, mix together 3 tablespoons of BBQ sauce, 3 tablespoons of real maple syrup, and 2 tablespoons of soy sauce. Set aside.
Heat a large, heavy pan or wok over high heat with 1 tablespoon of oil. Add thinly sliced beef to the hot pan in a single layer and sauté without disturbing for 2-3 minutes. Stir and sauté for an additional 2 minutes or until the beef is nearly cooked through. Lightly season with salt and pepper, then add ginger and garlic and sauté for 1 minute.
Pour the desired amount of sauce over the beef (I added 5 tablespoons) and stir-fry for another 1 minute or until fully cooked through. Transfer the beef to a plate and cover to keep warm. Wipe the pan clean with a damp paper towel.
Put the same pan over high heat and add 1 tablespoon of oil. Once hot, add mushrooms, lightly season with salt and pepper, and stir-fry until golden brown (about 5 minutes). Then, remove the mushrooms and transfer them to the plate with the beef.
Add 1 tablespoon of oil, sliced onion, and vegetables to the pan, and stir-fry for 8 minutes or until they are softened and golden brown.
Mix the vegetables with the beef and mushrooms, then drizzle in more sauce to taste (I added another 2 tablespoons), and stir-fry just until everything is heated through.
Serve the beef stir fry hot with a side of steamed white rice. Enjoy your delicious homemade meal!