Preheat your oven to 400°F and line a large baking sheet with parchment paper.
Toss the sliced zucchini, chopped red bell pepper, and cherry tomatoes with 0.5 tbsp of olive oil, salt, and pepper.
Spread the vegetables in a single layer and roast for 18 minutes until the tomatoes are blistered and the zucchini is tender.
While vegetables roast, season the chicken breast evenly on both sides with dried oregano, dried basil, and the remaining salt and pepper.
Heat the remaining 0.5 tbsp of olive oil in a large skillet over medium-high heat.
Add the chicken to the skillet and sear for 6 to 7 minutes per side until golden brown and the internal temperature reaches 165°F.
Stir the minced garlic into the skillet during the last minute of cooking, sautéing until fragrant but not browned.
Drizzle the balsamic vinegar into the skillet to glaze the chicken, then serve immediately alongside the roasted vegetables with a sprinkle of parmesan cheese.