Juice one of the lime; cut the other half into wedges.
Soak the noodles in very hot water for about ten minutes to soften them.
Combine the fish sauce, sugar, vinegar, and ketchup, stir to dissolve. (This may be easier to do if you warm the mixture in a microwave oven.)
Slice the scallions into small pieces, combine with the bean sprouts.
Stir fry the shrimp and garlic in the oil until cooked, about two minutes. Add the noodles to the wok, toss to mix the shrimp and oil into the noodles.
Add the liquid from step 2, folding it into the noodles. Lower the heat and cook a few minutes until most of the sauce has been absorbed by the noodles.
Using the wok spatula, lift one side of the noodles away from the surface of the wok, break an egg and let it slide under the noodles. Break the yolk, then cover the egg with noodles. Do the same with the other egg on the other side of the noodles. Let the eggs and noodles cook over moderate heat until the egg is set.
Fold the eggs into the noodles, being careful not to break the noodles. They'll be fairly fragile at this point.
Add the scallions, bean sprouts, lime juice, most of the ground peanuts, and half the fresh coriander the wok. Toss to mix all the ingredients, heat through.
Remove the noodles to a serving dish, garnish with the remaining peanuts and coriander.