Sprinkle the bottom of a large, shallow baking dish with 1 teaspoon salt and 3/4 teaspoons pepper. Place the squash flesh side down in the pan and add enough water to come up about 1/4-inch. Cover tightly with aluminum foil and cook in the oven until the squash is just fork tender, 1 to 1 1/2 hours. Shred the squash with a fork and transfer to a large heat proof bowl.
In a large saute pan, over medium heat, cook the bacon until it becomes a light brown but is not yet crispy. Pour off most of the fat and then add the shallots and garlic. Saute for 1 minute until the garlic and shallots are fragrant and begin to caramelize. Add the white wine and cook until the liquid has completely evaporated.
In a medium bowl, whisk the eggs together with the cheese and the parsley. Season with the remaining salt and pepper. Combine the eggs with the bacon mixture, warming the eggs in the pan. (Do not let the eggs cook through.) Add the spaghetti squash and toss to thoroughly combine and until squash is heated through. Adjust seasoning, if necessary and serve immediately.