Preheat oven to 425°F. Toss cauliflower with oil, and 1/4 tsp. each of the salt and black pepper. Spread in a single layer on a rimmed baking sheet. Brush with half of the BBQ sauce. Bake for 30 minutes, tossing once halfway through. Brush with remaining BBQ sauce.
While cauliflower bakes, combine tahini, cilantro, garlic, lemon juice, cumin, and remaining 3/4 tsp. salt and 1/4 tsp. black pepper in a small food processor or blender; blend until texture is similar to pesto. With motor running, gradually drizzle in 5 Tbsp. water and blend until sauce is light green and creamy.
Assemble tacos by filling toasted tortillas evenly with BBQ cauliflower. Top with shredded red cabbage and sliced avocado, and drizzle with green tahini sauce. Garnish with extra cilantro leaves, if desired.