Bring a large pot of salted water to a boil. Cook spaghetti until al dente according to package instructions. Reserve ¼ cup of the pasta water before draining. Set pasta aside.
In a large skillet over medium heat, cook the chopped bacon until crispy. Remove with a slotted spoon and drain on paper towels. Leave a small amount of bacon fat in the skillet.
Add olive oil to the skillet. Season chicken with salt, pepper, and garlic powder, then cook until golden and cooked through, about 6–7 minutes. Remove and set aside.
In the same skillet, reduce heat to low. Add minced garlic and cook for 30 seconds until fragrant. Stir in heavy cream and Parmesan cheese, mixing until melted and smooth.
In a small bowl, whisk together the egg yolks. Slowly whisk in a few spoonfuls of the hot cream sauce to temper the yolks, then pour the mixture back into the skillet, stirring constantly to avoid scrambling.
Add the cooked pasta, chicken, and bacon back into the skillet. Toss everything gently until well coated. Use reserved pasta water to loosen the sauce if needed.
Plate the pasta and garnish with chopped parsley and extra Parmesan if desired. Serve immediately for the best texture.