Preheat oven to 400 degrees Fahrenheit and line a baking sheet with parchment paper.

Halve the spaghetti squash lengthwise, remove seeds, brush with olive oil and salt, and roast cut-side down for 40 minutes until tender.

In a medium bowl, whisk together the eggs, egg yolks, and grated Pecorino Romano until smooth.

In a large skillet over medium heat, sauté the guanciale until the fat has rendered and the meat is crispy.

Once the squash is cooked, use a fork to shred the flesh into strands and add them to the skillet with the guanciale.

Add the diced chicken breast to the skillet and toss over low heat for 2 minutes to incorporate the fats.

Remove the skillet from the heat source to prevent the eggs from curdling.

Pour the egg and cheese mixture over the squash while tossing continuously until the residual heat creates a creamy emulsified sauce.

Season with extra black pepper and serve immediately.