Prepare the Pasta: Start by bringing a large pot of salted water to a vigorous boil. Add the pasta and cook according to the package instructions until it reaches an al dente texture. Remember to reserve 1/2 cup of the starchy pasta water before draining the rest of the pasta. Set the drained pasta aside.
Cook the Chicken: While the pasta is cooking, generously season both sides of the chicken breasts with salt and pepper. In a large skillet, heat the olive oil over medium-high heat until shimmering. Carefully place the chicken breasts in the skillet and cook for about 6-7 minutes per side, or until they are golden brown and fully cooked through. Once done, remove the chicken from the skillet and let it rest for a few minutes before slicing it into thin strips.
Sauté Garlic and Tomatoes: Using the same skillet, reduce the heat to medium and add the minced garlic. Sauté for approximately 30 seconds or until the garlic becomes fragrant, making sure not to burn it. Next, add the halved cherry tomatoes to the skillet and cook for about 3-4 minutes, stirring occasionally, until the tomatoes begin to soften and burst slightly.
Create the Sauce: Lower the heat further, and add the Boursin cheese along with the heavy cream to the skillet. Stir continuously until the cheese is melted and the mixture is velvety smooth. If the sauce is thicker than desired, gradually stir in a bit of the reserved pasta water until you achieve a creamy consistency.
Combine Ingredients: Add the cooked pasta and fresh spinach into the skillet with the creamy sauce. Gently toss all the ingredients together until the pasta is thoroughly coated in the cheese sauce. Fold in the sliced chicken and allow it to heat through for an additional minute.
Serve: Conduct a taste test and adjust the dish with additional salt and pepper if needed for desired seasoning.