Bring a large pot of salted water to a boil and cook the whole wheat spaghetti according to package directions until al dente.
While the pasta cooks, dice the chicken breast into small bite-sized pieces and season with a pinch of sea salt.
Heat the olive oil in a large skillet over medium heat, then add the chicken and cook until golden brown and cooked through.
Add the minced garlic to the skillet with the chicken and sauté for 1 minute until fragrant, then turn the heat to low.
In a small bowl, whisk together the egg and grated parmesan cheese until well combined.
Reserve about 1/4 cup of the starchy pasta water, then drain the spaghetti.
Add the hot spaghetti to the skillet with the chicken and garlic, tossing to combine.
Remove the skillet from the heat entirely to prevent the eggs from scrambling.
Slowly pour the egg and cheese mixture over the pasta while tossing constantly, adding a splash of pasta water as needed to create a silky sauce.
Season with the remaining sea salt and plenty of black pepper, then garnish with fresh parsley before serving.