Step 1: Preheat oven to 400°F (200°C). In a small bowl, mix minced garlic, parsley, thyme, 1 tbsp olive oil, salt, and pepper. Rub mixture evenly over chicken breasts.
Step 2: Toss carrot pieces with remaining 1 tbsp olive oil, salt, and pepper. Spread on a baking sheet in a single layer.
Step 3: Place chicken breasts on another baking sheet. Roast chicken and carrots in preheated oven for 20-25 minutes, until chicken is cooked through (internal temp 165°F) and carrots are tender and caramelized.
Step 4: While chicken and carrots roast, place potatoes in a pot, cover with water, and bring to a boil. Cook for 15-20 minutes until fork-tender.
Step 5: Drain potatoes and return to pot. Add heavy cream, 2 tbsp butter, milk, and Parmesan cheese. Mash until smooth and creamy. Season with salt and pepper.
Step 6: Remove chicken and carrots from oven. Let chicken rest for 5 minutes before slicing.
Step 7: Serve sliced chicken over creamy mash with roasted carrots on the side. Drizzle with pan juices if desired.