Preheat the oven to 350 degrees. Fill a large baking dish with about 1/4 inch of water. Season the cut sides of the squash with salt and pepper. Place, cut side down, in the dish and cover tightly with foil. Bake until the squash is tender, about 1 hour. Transfer to a work surface, cut side up; let cool slightly. Using a fork, scrape out the flesh, separating it into long strands.
Meanwhile, in a large skillet, cook the pancetta over medium heat, stirring occasionally, until browned and crispy, about 10 minutes. Using a slotted spoon, transfer to a plate. Pour off all but 1 tbsp. of the drippings. Add the onion to the skillet and cook over medium heat, stirring often, until translucent, 4 to 5 minutes. Add the cream and milk and bring to a simmer, scraping up the browned bits from the bottom of the pan.
In a medium bowl, whisk the eggs to blend. Gradually add the cream mixture, whisking constantly. Return the mixture to the skillet; add half the pancetta and 1/2 cup cheese. Stir until the cheese melts; season.
Add the spaghetti squash to the skillet and toss to coat; season. Divide among bowls and top with the remaining pancetta and cheese.