Bring a large pot of salted water to a boil. Add the broccoli and cook until just crisp-tender. Plunge into an ice bath to stop the cooking. Drain and reserve.
Bring a large pot of salted water to a boil and cook the pasta according to the package directions. Drain and reserve.
Place the oven rack in the middle position and preheat the oven to high broil.
Create a standard breading station in 3 separate 8-by-8-inch pans: Combine the flour, 1 tablespoon salt and 2 teaspoons pepper into the first pan. Whisk together the eggs and the milk in the second pan. Place the breadcrumbs in the third pan.
Trim any fat from the edges of the chicken breast and place each breast between 2 pieces of plastic wrap. With a meat mallet, pound out each breast until it is an even 1/4 inch thick.
Dredge each breasts using the standard breading: First in the flour, then in the egg wash and finally in the breadcrumbs, making sure to coat the entire breast.
Heat a large skillet over high heat until it begins to smoke and then reduce the heat to medium. Add 2 tablespoons oil to the pan and gently place 2 breasts in the pan. Cook the chicken on the first side until the breading is golden brown, about 5 minutes. Gently turn the breasts over and cook until the breading is golden brown on the other side, about 5 minutes. Remove the chicken breasts to a pan lined with paper towels. Repeat with the remaining chicken breasts, changing the oil between each batch.
Place the chicken breasts on rimmed baking sheets. Top each breast with 3 pieces of the broccolini and 2 slices of the mozzarella. Bake until the cheese is melted and begins to brown, 5 to 10 minutes.
For plating: Bring the Tomato Sauce to a simmer in a large skillet. Add the pasta and cook until the pasta and sauce are hot.
Divide the pasta and sauce among 6 plates, mounding it in the center of each plate. Place a finished chicken breast on top of each mound. Sprinkle each plate with 1 tablespoon Parmesan and 1 teaspoon chopped parsley.
Combine the whole tomatoes and their liquid, the olive oil, onion, basil, oregano, salt, pepper and 4 cloves garlic in a large bowl or 2-gallon container and puree with an immersion blender until smooth.
Heat a large saute pan over high heat until it begins to smoke. Reduce the heat to medium, add the grapeseed oil and remaining 4 cloves garlic and quickly saute. Add the diced tomatoes and saute for 1 to 2 minutes. Add the pureed tomato sauce and bring to a simmer. Cook for 15 minutes, remove from the heat. Bring back to a simmer when you are ready to plate. Yield: 6 servings