Pad Thai with Egg Noodles

Name: Pad Thai with Egg Noodles
Ingredients: 3 1/4 cups (1 lb./500 g) all-purpose flour; 2 eggs; 6 Tbs. water; 1 Tbs. canola oil; 1 lb. (500 g) large shrimp, peeled and deveined; 3 eggs, lightly beaten; 1/2 cup (4 fl. oz./125 ml) pad Thai noodle sauce, plus more, to taste; 2 green onions, white and light green portions, sliced; 2 carrots, peeled and julienned; 1 cup (4 oz./125 g) bean sprouts; 1/4 cup (1 oz./30 g) chopped unsalted roasted peanuts; Cilantro leaves for garnish; Lime wedges for serving