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 pancetta and place it in a cold skillet. Turn the heat to medium and cook until the fat renders and the pancetta is golden and crispy.
In a small bowl, whisk together the large egg, grated Pecorino Romano cheese, and black pepper until well combined.
Slice the pre-grilled chicken breast into thin strips and set aside.
Just before the pasta is finished, reserve 0.25 cup of the starchy pasta water.
Drain the pasta and immediately add it to the skillet with the pancetta, turning off the heat to ensure the eggs do not scramble.
Quickly pour the egg and cheese mixture over the hot pasta, tossing constantly with tongs. Add a splash of the reserved pasta water as needed to create a creamy, emulsified sauce.
Fold in the grilled chicken strips and baby spinach, allowing the residual heat to wilt the spinach and warm the chicken.
Serve immediately in a warm bowl with an extra crack of black pepper.