Begin by bringing a large pot of salted water to a roaring boil. Add bow-tie pasta and cook for 8-10 minutes until al dente. Reserve about ½ cup of the starchy pasta water just before draining, then drain the pasta and set aside.

While the pasta cooks, cut boneless, skinless chicken into ½-inch chunks and season generously with salt and pepper. Dredge each piece in all-purpose flour, shaking off any excess.

In a large skillet, heat 2 tablespoons of unsalted butter and 1 tablespoon of extra-virgin olive oil over medium-high heat until the butter is melted and bubbling. Carefully add the coated chicken to the skillet in a single layer and sauté for 5-7 minutes or until golden brown and cooked through.

Reduce the heat to medium, and add the chopped shallot to the skillet, sautéing for about 1-2 minutes until softened. Stir in minced garlic and cook for another 30 seconds.

Pour in the chicken stock and bring to a gentle simmer, scraping up any brown bits. Allow to simmer for about 3-5 minutes, or until the liquid has reduced by half.

Stir in the remaining 2 tablespoons of unsalted butter, fresh lemon juice, and capers. Allow to simmer for another minute, then taste and adjust seasoning.

Return the cooked chicken to the skillet and add the drained pasta, tossing to ensure an even coating of sauce. Stir in some reserved pasta water until reaching desired consistency.

Serve immediately on warm plates, garnished with freshly chopped parsley.