Sauté bacon in large skillet over medium heat until crisp. Transfer to paper towels. Pour off all but 1 tablespoon drippings; add 3 teaspoons oil and maintain heat. Add onions; sauté until deep golden brown, about 20 minutes. Stir in crushed red pepper. Season with salt and pepper. Remove from heat; cover to keep warm.
Meanwhile, cook pasta in pot of boiling salted water until tender but still firm to bite. Drain, reserving 1/2 cup pasta cooking liquid in bowl. Return pasta to pot; add onions. Cover to keep warm.
Heat remaining oil in large skillet over medium heat. Crack eggs into skillet; fry until whites are set but yolks are still soft, about 4 minutes. Add spinach, cheese, eggs, and bacon to pasta; toss until egg whites are torn into shreds and spinach wilts. Add pasta cooking liquid to moisten. Season with salt and pepper; serve.
