Bring a large pot of salted water to a rolling boil. Add the pasta and cook for one minute less than the package instructions for al dente texture. Reserve 250 milliliters (1 cup) of pasta water prior to draining. Set the cooked pasta aside.

In a large skillet or Dutch oven, heat the olive oil and unsalted butter over medium heat until the butter has melted. Add the diced chicken in a single layer and sauté for approximately 6 to 7 minutes, turning occasionally, until the chicken is golden brown and fully cooked. Transfer the cooked chicken to a plate and loosely cover.

Reduce the heat to medium-low. In the same skillet, add the diced shallot and minced garlic. Sauté for 1 to 2 minutes until softened and aromatic. Stir in the tomato paste and cook for an additional minute, allowing it to caramelize slightly. Pour in the chicken stock, deglazing the pan by scraping any browned bits from the bottom. Bring the mixture to a gentle simmer.

Add the softened cream cheese to the skillet. Whisk continuously until the cream cheese has fully melted and the mixture is smooth, approximately 2 to 3 minutes. Stir in the buffalo wing sauce and ranch dressing until thoroughly combined.

Return the cooked chicken and drained pasta to the skillet. Toss gently to coat the pasta and chicken with the sauce. If the mixture appears too thick, gradually add the reserved pasta water, one tablespoon at a time, until the desired consistency is reached.

Sprinkle the grated sharp cheddar and Monterey Jack cheeses over the pasta. Fold gently until the cheeses melt completely, resulting in a creamy, velvety sauce. Season with kosher salt and freshly ground black pepper to taste.

Transfer the pasta to serving bowls. Garnish with freshly chopped parsley or additional buffalo sauce, if desired. Serve warm.