In a non-stick pan over medium heat, cook the bacon until crispy. Transfer to a bowl and set aside. Reserve 1 tablespoon of bacon grease, discarding the rest. Set the pan aside for later use.

In a medium bowl, whisk together the egg yolks, grated cheese, pumpkin purée, ground nutmeg, 1 pinches of salt, 1/4 teaspoon black pepper, and the reserved bacon grease until smooth and well combined.

Cook spaghetti according to package instructions until al dente. Reserve 1 cup of pasta water, then drain.

Add the pasta back to the pan used for the bacon. Stir in the cooked bacon and the egg-pumpkin mixture, tossing to coat over very low heat. Gradually add the reserved pasta water, a little at a time, until the sauce becomes creamy and clings to the pasta.

Taste and adjust seasoning with more salt or black pepper if needed. Serve immediately and enjoy!