Roast the squash: Preheat your oven to 425°F. Toss squash cubes with 2 tablespoons olive oil, salt, and pepper on a baking sheet. Spread in a single layer and roast for 25-30 minutes until very tender and caramelized at the edges, stirring halfway through.
Prepare the pasta water: Bring a large pot of heavily salted water to a boil. The water should taste like the sea – this is crucial for properly seasoning the pasta.
Blanch the broccoli rabe: Add the chopped broccoli rabe to the boiling water and cook for 2 minutes until bright green and slightly tender. Using tongs or a slotted spoon, transfer to a colander (keep the water boiling for your pasta). Rinse briefly with cold water to stop cooking, then drain well.
Cook the pancetta: In a large skillet over medium heat, cook the diced pancetta until crispy, about 5-7 minutes. Remove with a slotted spoon to a paper towel-lined plate, leaving the fat in the pan.
Sauté the aromatics: Add remaining tablespoon of olive oil to the pancetta fat. Add onion and cook until softened, about 4 minutes. Add garlic and cook 1 minute more until fragrant. Add the blanched broccoli rabe and sauté for 2-3 minutes until tender. Season with salt and pepper. Remove from heat and set aside.
Cook the pasta: Add pasta to the boiling water and cook until al dente according to package directions. Reserve 1½ cups of pasta water before draining.
Blend the squash: While pasta cooks, transfer roasted squash to a blender or food processor. Add ½ cup of the reserved pasta water and blend until very smooth. The consistency should be like a thick sauce – add more pasta water if needed.
Prepare the egg mixture: In a medium bowl, whisk together eggs, egg yolk, both cheeses, nutmeg, and ¼ teaspoon each salt and pepper until well combined.
Combine everything: Return the drained pasta to its pot over low heat. Quickly add the squash puree and ¼ cup pasta water, tossing continuously. Remove from heat completely, then immediately add the egg mixture, continuing to toss vigorously to create a creamy sauce (the residual heat will cook the eggs). If sauce seems too thick, add more reserved pasta water a tablespoon at a time.
Finish the dish: Fold in the broccoli rabe mixture and crispy pancetta. Taste and adjust seasoning with salt and pepper. Serve immediately, topped with additional grated cheese and red pepper flakes if desired.