Arrange a rack in center of oven; preheat to 400°. Cut spaghetti squash in half lengthwise and pick out seeds. Rub inside of squash with 1 Tbsp. oil; season with salt. Arrange cut side down on a baking sheet.
Roast squash until tender and browned, 35 to 45 minutes. Let cool slightly.
Using 2 forks, shred spaghetti squash strands from shell. Place in a fine-mesh strainer set over a bowl and gently press to expel as much liquid as possible.
In a medium skillet over medium-low heat, cook pancetta, stirring occasionally, until browned and crispy, 10 to 12 minutes. Remove pan from heat.
In a large heatproof bowl, whisk egg, egg yolks, cheese, and pepper.
Add spaghetti squash to pancetta in skillet and return to medium heat. Cook, tossing with tongs occasionally, until squash is thoroughly heated through (it should be steaming and hot to the touch) and pan is completely dry, 1 to 2 minutes.
Add hot spaghetti squash and pancetta to egg yolk mixture in bowl. Working quickly, toss until combined and glossy.
Divide squash carbonara among bowls. Top with more cheese; season with pepper (if desired).
