Season the chicken breasts with salt and pepper. Heat the olive oil in a grill pan over medium-high heat. Grill the chicken for 5-7 minutes on each side, or until fully cooked and no longer pink in the center. Let rest for a few minutes, then slice.
Cut the avocado in half, remove the pit, and scoop the flesh into a bowl. Mash it with a fork until smooth. Add a squeeze of lemon juice, salt, and pepper to taste.
In a large skillet over medium heat, cook the pancetta or guanciale until crispy. Add the minced garlic and cook for an additional minute.
Add the cooked spaghetti to the skillet with the pancetta. Toss to coat the pasta in the rendered fat. Remove the skillet from heat.
Quickly pour the egg and cheese mixture into the pasta, tossing vigorously to create a creamy sauce. Add reserved pasta water a little at a time to reach the desired consistency.
Arrange the sliced tomatoes and mozzarella over the sauce.
Season with salt and pepper to taste. Garnish with fresh parsley if desired. Serve immediately.
Notes
For extra flavor, you can sprinkle some grated Parmesan cheese over the pizza before baking.