Remove ends and strings from green beans.
Cut crosswise in 1/8 inch-thick diagonal slices.
Heat a wide frying pan over high heat.
When pan is hot, add 2 tablespoons of the oil.
When oil begins to heat, add garlic.
Stir once, then add shrimp and stir-fry for 1 minute.
Add beans and carrot, reduce heat to medium, and stir-fry until vegetables are crisp-tender (about 2 minutes).
Remove from pan and cool.
Prepare foo yung sauce.
Beat eggs with salt and pepper, then stir in cooled shrimp-vegetable mixture.
Heat 2 more tablespoons oil in pan over medium-high heat.
When oil is hot, measure 1/4 cup of egg mixture for each patty, cook like pancakes, and make 3 or 4 at a time.
When egg is set, turn to cook other side.
Fry until golden.
Remove to a heated serving platter and keep warm.
Repeat until all patties have been cooked, adding more oil as needed.
Pour hot foo yung sauce over patties and serve at once.