Fill a large pot with water and bring to a full rolling boil. Season very generously with salt.

Heat a large skillet or Dutch oven over medium heat. Add the chopped bacon and cook until crisp and deep golden, about 3 to 5 minutes. Remove with a slotted spoon and drain on paper towels. Leave 1 to 2 tablespoons of bacon fat in the pan.

While the bacon cooks, whisk together the egg yolks, Parmesan cheese, heavy cream, salt, and pepper in a medium bowl until completely smooth. Set aside next to the stove.

Pat the chicken tenders dry with paper towels. Season both sides with salt and pepper. Cook in the bacon fat over medium heat until golden brown and cooked through to an internal temperature of 165 degrees F, about 2 to 3 minutes per side. Transfer to a plate to rest, then slice.

Drop the spaghetti into the boiling water and cook just under al dente, about 8 to 10 minutes. Reserve at least 1/2 cup of starchy pasta water before draining.

Lower the heat to medium-low and add the minced garlic to the skillet. Cook for 1 to 2 minutes until fragrant and just starting to turn golden.

Using tongs, transfer the drained spaghetti directly into the skillet with the garlic. Toss well to coat every strand in the pan drippings.

Pull the pan completely off the heat. Pour in the egg and cheese mixture while tossing the pasta nonstop. Once the sauce starts to thicken and turn glossy, return the pan to the lowest heat setting and keep tossing for 2 to 3 more minutes. Add pasta water a splash at a time if the sauce tightens too much. Do not increase the heat or the eggs will scramble.

Add the crispy bacon back into the pan and toss to combine. Taste and adjust salt and pepper. Arrange the sliced chicken on top and serve immediately.