In a medium bowl, combine the pork with the onion, carrot, garlic, salt, and pepper and mix with your hands until evenly combined. Position 1 spring roll wrapper in front of you like a diamond (so that a point is facing you), and place 1 tablespoon of filling on the diamond's bottom half. Lift the point nearest you and wrap it around the filling. Fold the left and right corners in toward the center, brush the top tip with some of the beaten egg, and continue rolling into a tight cylinder. Transfer to a parchment paper—lined baking sheet and repeat with the remaining wrappers and filling.
Make the dipping sauce: In a small jar, combine the vinegar, soy sauce, sugar, peppercorns, garlic, and chiles. Shake to mix.
Pour oil to a depth of 2 inches in a 6-quart Dutch oven, attach a deep-fry thermometer to the side of the pan, and heat to 350°. Working in batches, add the spring rolls to the oil and fry until golden brown and the filling is cooked, about 8 minutes. Using a slotted spoon, transfer the lumpia to paper towels to drain. Season with salt and serve while hot with the garlic-chile vinegar sauce.