Prep tempeh: You can do this the day before and let the tempeh marinate overnight, so you can throw together the bibimbap in about 30 minutes. Add tempeh to a saucepan filled with 1-2 inches of water. Bring to a simmer and cook for 10 minutes.
Make tempeh marinade: In a shallow dish or ziplock bag, mix together gochujang, soy sauce, Worcestershire sauce, vinegar, sesame oil, and garlic. Add tempeh and marinate at least 30 minutes, or overnight.
Bake tempeh: Preheat oven to 400°F. Line a baking sheet with parchment paper. Place tempeh cubes on parchment paper (shake off excess marinade), keeping some space between the tempeh so they crisp up. Brush the tops with marinade. Bake 10 min, flip tempeh over and brush with marinade. Bake for another 10-15 minutes or until golden and crispy.
While the tempeh is baking, prepare the bibimbap toppings: Cook carrots, mushrooms, and zucchini separately (technically you can cook them all together, but the presentation of your bibimbap won't be as nice). Heat oil in a pan, then add veggie and salt/soy sauce. Cook until tender.
Make sauce: Mix together gochujang, Japanese Worcestershire sauce (or sugar), sesame oil, and vinegar. Taste and adjust seasonings as desired.
Build bibimbap bowls: Place steamed rice on the bottom of your bowls. Top with cucumbers, bean sprout salad, carrots, mushrooms, zucchini, and tempeh. Drizzle with sauce, mix, and dig in! You can also garnish with some toasted sesame seeds.