Preheat your oven to 425°F (220°C). On a baking sheet, toss the broccoli florets and sliced carrots with olive oil, salt, and pepper. Spread them out evenly and roast in the oven for 15–20 minutes.

While the vegetables are roasting, bring 4 cups of chicken broth to a boil in a large pot. Add the bowtie pasta and cook according to package instructions, approximately 10–12 minutes, until al dente. Reserve 1 cup of pasta water before draining.

In a large skillet, heat remaining olive oil over medium heat. Season chicken breasts with salt and pepper, then add to skillet. Cook for 6–7 minutes on each side until golden brown. Remove and slice into strips.

In the same skillet, add minced garlic and sauté for about 1 minute. Pour in heavy cream and bring to a gentle simmer. Gradually whisk in cheddar and Havarti cheese until smooth.

Add cooked pasta, roasted broccoli, carrots, and sliced chicken to the sauce. Toss gently to coat, cooking on low for another 2–3 minutes.

Garnish with freshly chopped parsley and additional cheese if desired. Serve warm.