Preheat the oven to 400°F.
Season the boneless chicken thighs with olive oil, lemon juice, minced garlic, salt, and pepper. Toss the cubed butternut squash with olive oil, salt, and pepper. Place both on a baking sheet with 4 whole garlic cloves. Roast for 30-40 minutes, until the chicken is cooked through and the squash is tender.
Cook the rigatoni in salted boiling water according to package directions. Reserve ½ cup of the pasta water before draining.
Quickly broil the chicken and squash on high for 3-4 minutes for a beautiful golden color.
Blend the roasted squash and roasted garlic cloves with chicken broth until smooth. Pour into a pan over medium heat and stir in the heavy cream, and half of the grated parmesan cheese. Season with salt and pepper.
Dice the roasted chicken and add it to the pasta. Toss everything with the butternut squash sauce, using pasta water you saved earlier to adjust consistency if needed.
Finish with plenty of finely grated parmesan and fresh thyme or parsley. Serve warm.