Bring a medium pot of salted water to a boil and cook the whole wheat spaghetti according to package directions until al dente.
Reserve 0.25 cup of the starchy pasta water before draining the noodles.
While the pasta cooks, dice the chicken breast into small, bite-sized pieces and mince the garlic clove.
In a small bowl, whisk together the whole egg, egg whites, grated Pecorino Romano, and the black pepper until well combined.
Heat a large skillet over medium heat, add the pancetta, and cook until the fat renders and the meat becomes crispy.
Add the diced chicken to the skillet with the pancetta and sauté until the chicken is golden and cooked through.
Stir in the minced garlic and cook for 30 seconds until fragrant, then remove the skillet from the heat source.
Add the hot, drained pasta to the skillet, tossing it quickly with the chicken and pancetta to coat.
Slowly pour the egg and cheese mixture over the pasta while tossing constantly; the residual heat will create a creamy sauce without scrambling the eggs.
Thin the sauce with a splash of reserved pasta water if needed and garnish with fresh parsley before serving.