Heat oven to 375° F. Coat a 2-quart baking dish with nonstick cooking spray. Bring a large pot of lightly salted water to boiling.
Cook bacon in a nonstick skillet over medium heat until just crisp, 10 minutes. Drain on a paper towel-lined plate.
Meanwhile, cook spaghetti 9 minutes in boiling water. Drain and return to pot.
In a large bowl, whisk together eggs and yolks. Add 2/3 cup of the cheese, the milk, half-and-half, parsley, salt and pepper. Toss sauce with pasta in pot along with bacon. Transfer to prepared dish and top with remaining 2 tbsp Parmesan.
Bake at 375° F for 35 minutes. Cool 10 minutes, then cut into wedges.