In a large pot, bring salted water to a rolling boil over high heat. Add your chosen pasta, cooking it according to package instructions until al dente, which usually takes about 8-10 minutes. Reserve ½ cup of pasta water before draining the rest and set aside.

Season both sides of the sliced chicken breasts with salt and pepper. In a large skillet, heat olive oil and butter over medium-high heat. Add the chicken and cook for 5-6 minutes per side until golden brown and cooked through. Remove from skillet and let rest before slicing.

Reduce heat to medium and sprinkle in flour, whisk for about a minute to prevent lumps. Gradually pour in chicken broth, stirring continuously to deglaze the skillet. Add heavy cream, pesto, lemon juice, and chopped sun-dried tomatoes, stirring until well combined and thickened for about 3-4 minutes.

Once the sauce has thickened, stir in fresh baby spinach until it wilts, about 2 minutes. Fold in the drained pasta, ensuring it's evenly coated in sauce. Add reserved pasta water if the sauce is too thick.

Taste and adjust seasoning. Return sliced chicken to the skillet and toss everything until heated thoroughly. Serve hot, topped with freshly grated Parmesan for added richness.