Bring a large pot of salted water to a rolling boil over high heat. Once boiling, add the bowtie pasta and cook according to the package directions until al dente, usually around 10-12 minutes. Stir occasionally to prevent sticking, then drain the pasta and set it aside in a large bowl to cool slightly.

While the pasta cooks, season the chicken breasts generously with salt and pepper. Heat a large skillet over medium-high heat and add olive oil. Once shimmering, place the chicken breasts in the skillet and cook for about 5-7 minutes per side, or until golden brown and fully cooked, reaching an internal temperature of 165°F. Remove from the skillet and let rest while you prepare the sauce.

In the same skillet, reduce the heat to medium and add butter. As it melts, add minced garlic and sauté for about 1-2 minutes, stirring frequently, until fragrant but not browned.

Sprinkle flour into the skillet with the garlic and stir to combine, creating a roux. Cook this mixture for about 1 minute until it thickens slightly and forms a paste.

Gradually whisk in the milk and heavy cream into the roux, stirring continuously to prevent lumps. Cook for approximately 3-5 minutes on medium heat until the sauce thickens and begins to bubble gently.

Once thickened, reduce the heat to low and stir in freshly grated Parmesan and sharp cheddar cheese. Continue stirring until the cheeses are completely melted and incorporated.

Add the cooked bowtie pasta and sliced chicken into the cheese sauce, gently tossing to coat everything evenly.

Remove the skillet from heat and let the dish sit for a couple of minutes to allow the flavors to develop. Serve warm, optionally garnishing with additional Parmesan cheese or fresh herbs if desired.