Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
While the pasta is cooking, prepare the chicken. Preheat your oven to 400°F.
In a shallow bowl, beat the eggs and season with salt and pepper. In another shallow bowl, combine the breadcrumbs and grated Parmesan cheese.
Dip each chicken breast into the egg mixture, allowing excess to drip off, then coat with the breadcrumb and Parmesan mixture, pressing gently to adhere.
Heat olive oil in a large oven-safe skillet over medium heat. Add the breaded chicken breasts and cook for about 4-5 minutes on each side until golden brown.
Transfer the skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F.
In a large bowl, combine the cooked pasta and pesto, adding reserved pasta water a little at a time until you reach your desired consistency.
Slice the crispy Parmesan chicken and serve it over the pesto pasta. Garnish with fresh basil leaves if desired.