Preheat oven to 400F. Lightly grease a large sheet pan and set aside.
Cut each spaghetti squash in half and scoop out seeds. Rub interior of each half with olive oil and season with salt and pepper. Lay squash halves, cut side-down on prepared sheet pan and bake at 400F 25-30 minutes until squash is tender (you may have to roast longer if using larger spaghetti squash).
Allow squash to cool slightly, then use a fork to shred the inside of squash into noodles and place in a large bowl (do not discard the squash boats). Keep squash warm and set aside for a moment.
In a medium bowl, whisk egg yolks, egg, and Parmesan until completely smooth. Set aside for a moment.
In a Dutch oven or large skillet over medium heat, cook diced bacon or pancetta until crispy, stirring occasionally. Use a slotted spoon to transfer bacon to paper towels to drain.
Add garlic to bacon drippings in pan over medium heat and sauté 1 minute until fragrant. Add spaghetti squash noodles and 1/2 cup warm chicken broth to pan. Cook over medium heat 2-3 minutes until liquid mostly is absorbed. Remove from heat and allow to cool 1 minute.
Whisk remaining 1/4 cup warm chicken broth into egg yolks until smooth. Fold egg sauce into hot spaghetti squash mixture, folding with a wooden spoon until a creamy sauce forms and coats spaghetti squash.
Stir parsley and bacon into carbonara and season with salt and pepper to taste. Scrape spaghetti squash carbonara back into boats and top with additional grated Parmesan for serving. Enjoy!