Preheat the oven to 400°F (200°C).

On a large baking sheet, toss the cubed butternut squash and unpeeled garlic cloves with olive oil, salt, and pepper. Spread in a single layer.

Roast in the preheated oven for about 25-30 minutes, or until the squash is tender and lightly caramelized. Stir halfway through cooking.

While the squash is roasting, season the chicken breasts with salt, pepper, dried thyme, and smoked paprika.

In a large skillet over medium heat, add a little olive oil. Cook the chicken breasts for about 6-7 minutes on each side, or until they are cooked through and no longer pink in the center. Remove from skillet and let rest.

Cook the pasta according to package instructions. Drain and set aside.

Once the squash and garlic are roasted, squeeze the garlic out of its skins into a blender or food processor. Add the roasted squash, chicken broth, and heavy cream. Blend until smooth and creamy.

Slice the cooked chicken into bite-sized pieces and return to the skillet over low heat. Pour the creamy butternut squash sauce over the chicken and stir to combine.

Add the cooked pasta to the skillet, tossing to coat everything in the creamy sauce. Stir in the grated Parmesan cheese and mix until melted and well combined.

Serve hot, garnished with chopped fresh parsley.