Preheat oven to 400°F (200°C). Toss cherry tomatoes, zucchini, bell pepper, and red onion with 1 tablespoon olive oil, oregano, salt, and pepper.
Spread the vegetables on a baking sheet and roast for 20-25 minutes until tender and slightly charred.
Bring vegetable broth to a boil in a saucepan. Add orzo and cook according to package instructions until al dente, about 8-10 minutes, then drain any excess liquid.
Heat remaining 1 tablespoon olive oil in a small skillet over medium heat. Add minced garlic and cook for 1 minute until fragrant.
Stir garlic, lemon zest, and half the lemon juice into the cooked orzo. Season with salt and pepper.
Whisk together red wine vinegar, remaining lemon juice, fresh parsley, basil, and a pinch of salt to prepare the herb vinaigrette.
Divide lemon garlic orzo among bowls. Top with roasted vegetables and torn pieces of burrata cheese.
Drizzle herb vinaigrette over the bowls and serve immediately.