Bring a pot of salted water to a boil and cook the whole wheat spaghetti until al dente.
While pasta cooks, whisk the egg, egg yolk, and grated parmesan in a small bowl until smooth.
In a large skillet over medium heat, sauté the diced pancetta until crispy and the fat has rendered.
Add the diced chicken breast to the skillet with the pancetta and cook until golden and cooked through.
Stir in the minced garlic for 30 seconds until fragrant, then add the spiralized zucchini for 1 minute.
Reserve 1/4 cup of pasta water, then drain the pasta and add it to the skillet with the chicken and pancetta.
Remove the skillet from the heat immediately to prevent the eggs from scrambling.
Quickly pour in the egg mixture and reserved pasta water, tossing constantly until a velvety sauce forms.
Season with freshly ground black pepper and sea salt before serving immediately.