Preheat the oven to 400°F (200°C).
In a small bowl, mix together 2 tablespoons olive oil, garlic powder, paprika, dried thyme, 1/2 teaspoon salt, and 1/2 teaspoon black pepper.
Place the chicken breasts on a baking sheet lined with parchment paper or foil. Brush both sides of each chicken breast evenly with the seasoned olive oil mixture.
In a separate bowl, toss the baby carrots and broccoli florets with 1 tablespoon olive oil, 1/2 teaspoon salt, and 1/4 teaspoon black pepper.
Arrange the vegetables around the chicken breasts on the baking sheet.
Bake in the preheated oven for 30-35 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the vegetables are tender.
While the chicken and vegetables are baking, place the cubed potatoes and garlic cloves in a large pot and cover with cold water.
Bring to a boil over high heat, then reduce heat to medium and simmer for 15-20 minutes, or until the potatoes are fork-tender.
Drain the potatoes and garlic and return them to the pot.
Add the milk, unsalted butter, 1/2 teaspoon salt, and 1/4 teaspoon black pepper to the potatoes and garlic.
Mash until smooth and creamy.
Serve the baked chicken breasts with the roasted vegetables and garlic mashed potatoes on the side.