Sesame oil should be heated over medium-high heat in a big skillet. Add the shrimp and simmer for 1 to 2 minutes, or until the shrimp is almost cooked through.
Add scallions, ginger, and garlic. Sauté for about 30 seconds, or until aromatic. Add vinegar, soy sauce, and carrots to the mixture.
Cook vegetables for two to three minutes over high heat, or until they are crisp and tender. Place in a colander, drain, and allow to cool.
Place each egg roll wrapper one at a time with the points pointing in a diamond shape toward the top and bottom of the surface. Onto the bottom third of the wrapper, spoon 1/3 cup of the mixture.
Run your finger down the wrapper's edges after dipping it in a small dish of water. Lift the point closest to you, then encircle the filled with it.
Roll the paper into a tight cylinder while folding the left and right corners toward the center. Repeat with the remaining wrappers and filling after setting aside.
Spray oil evenly over the egg rolls' surfaces using your fingers.
Cook at 370°F in batches for 5–7 minutes, flipping once, or until golden brown.
Serve right away with optional dipping sauce on the side.