Preheat the oven to 425°F (220°C).
In a large bowl, combine the red bell pepper, yellow bell pepper, zucchini, yellow squash, red onion, and broccoli florets.
Drizzle 1 tablespoon of olive oil over the vegetables. Sprinkle with 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, dried rosemary, and paprika. Toss to coat evenly.
Spread the vegetables in a single layer on a large baking sheet. Roast in the preheated oven for 20-25 minutes, stirring halfway through, until vegetables are tender and slightly caramelized.
While the vegetables roast, pat the chicken breasts dry with paper towels.
In a small bowl, mix the remaining 1/2 teaspoon kosher salt, 1/4 teaspoon black pepper, garlic powder, and dried thyme.
Rub the spice mixture evenly over both sides of each chicken breast.
Heat the remaining 1 tablespoon of olive oil in a large skillet over medium-high heat.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, or until the internal temperature reaches 165°F (74°C) and the chicken is golden brown.
Remove the chicken from the skillet and let rest for 5 minutes.
Serve each chicken breast with a generous portion of the roasted vegetables.