Bring a pot of salted water to a boil and cook the whole wheat spaghetti according to package directions until al dente, reserving 1/4 cup of pasta water before draining.
While the pasta cooks, heat the olive oil in a large skillet over medium heat and add the diced pancetta, cooking until the fat renders and it becomes crispy.
Add the bite-sized chicken breast pieces to the skillet with the pancetta, seasoning with half the salt and pepper, and sauté until golden brown and cooked through.
Stir in the minced garlic and cook for 30 seconds until fragrant, then remove the skillet from the heat to prevent the eggs from scrambling later.
In a small bowl, whisk together the egg, Pecorino Romano cheese, and the remaining black pepper until well combined.
Toss the hot, drained pasta into the skillet with the chicken and pancetta, then quickly pour in the egg mixture and a splash of the reserved pasta water.
Stir vigorously and continuously until the sauce thickens into a creamy, glossy coating, adding more pasta water if needed to reach your desired consistency.
Garnish with fresh chopped parsley and the remaining sea salt before serving immediately.