Cook linguine according to package directions for al dente. Meanwhile, in a large skillet, heat 2 tablespoons oil and 1 tablespoon butter over medium heat until butter melts. Stir in garlic; cook until golden, about 1 minute. Add pepper flakes
Break two eggs and slip into skillet on top of garlic and pepper flakes. Reduce heat to low; cook until whites are completely set but yolks are still soft.
Drain water off of linguine; return to pan. Chop the cooked eggs up and stir egg/oil combination into cooked linguine; add 2 tablespoons of Parmesan cheese, salt and pepper, tossing to coat. Keep warm.
In the skillet, heat remaining oil and butter over medium heat. Break remaining eggs, one at a time, into skillet. Reduce heat to low; cook until whites are set and yolks begin to thicken, turning once if desired.
Serve pasta in individual bowls. Top with fried eggs, additional cheese for sprinkling and, if desired, parsley.