Preheat the oven to 450 degrees Fahrenheit. Drizzle 1 tablespoon olive oil on both sides of 2 ½ pounds boneless skinless chicken breast. Season it with salt and pepper to taste then place the chicken in a 13 x 9 x 2-inch baking dish.
Bake the chicken until it reaches an internal temperature of 165 degrees Fahrenheit, about 15 to 18 minutes.
Pesto
Place 1 cup packed basil and 1 cup packed baby spinach in a resealable plastic bag. Use a rolling pin to lightly bruise the herbs and greens. Transfer to a food processor or blender.
Heat a medium-sized skillet over medium heat. Toast 3 cloves unpeeled garlic until the outsides are lightly browned, shaking the pan occasionally, about 8 minutes. Remove the garlic skin and add it to a food processor.
Place ¼ cup walnuts in the same pan and toast over medium heat, 3 to 4 minutes. Transfer to the food processor.
Add ½ teaspoon kosher salt and ¼ teaspoon black pepper to the food processor. Process the pesto mixture by pulsing five times to help break down the greens.
Turn the food processor on low speed, as it's running slowly drizzle in ½ cup extra-virgin olive oil until a smooth pesto with some smaller pieces is formed, about 10 seconds from start to finish.
Add ¼ cup grated parmesan cheese to the pesto and process on low speed for 5 seconds. Taste and season the sauce with salt and pepper as desired. Transfer pesto to a small bowl.
Brush some pesto sauce on each cooked chicken breast. Transfer to a serving platter.
Top chicken with additional chopped walnuts and parmesan cheese, and 1 cup diced tomatoes. Serve extra pesto sauce on the side.