Preheat your grill to medium-high heat.
Brush the pizza crust with the olive oil and place it on the grill. Grill for 3-4 minutes, or until the crust is golden brown and crispy.
Meanwhile, heat a large skillet over medium-high heat. Add the bell peppers, onion, garlic, and mushrooms and cook until the vegetables are tender, about 5 minutes.
In a small bowl, whisk together the honey, jalapeno pepper, and chili powder.
Once the crust is done, spread the vegetables over the top. Drizzle the spicy-honey glaze over the vegetables
Sprinkle the mozzarella cheese over the top and place the pizza back on the grill. Close the lid and cook for another 5 minutes, or until the cheese is melted and bubbly.
Remove the pizza from the grill and sprinkle with fresh basil. Slice and serve.