Bring a pot of salted water to a boil and cook the whole wheat spaghetti according to package directions until al dente. Drain and set aside, reserving a splash of pasta water.
While the pasta cooks, finely mince the garlic. In a medium skillet over medium heat, add the pancetta and cook until it becomes crispy and golden. Remove the pancetta with a slotted spoon and transfer to a paper towel-lined plate to drain any excess fat.
Lower the heat and add the minced garlic to the pancetta fat in the skillet. Sauté for about 30 seconds until fragrant, being careful not to burn it.
In a bowl, whisk together the whole egg and egg whites. Add a pinch of salt, pepper, and dried oregano.
Add the drained spaghetti to the skillet with garlic, tossing to coat in the pancetta fat. Remove from heat and immediately pour in the egg mixture, stirring briskly to create a creamy sauce without scrambling the eggs. If needed, add a small splash of the reserved pasta water to achieve a silky consistency.
Stir in the crispy pancetta and fresh baby spinach, allowing the residual heat to wilt the spinach slightly.
Serve immediately with an extra sprinkle of pepper and oregano if desired.