Warm 2 Tbsp. oil in a large skillet over medium-high heat. Add garlic, ginger and scallions. Sauté until fragrant but not browned, about 1 minute. Add slaw mix and bean sprouts and sauté until wilted, about 5 minutes. Season with salt and pepper. Let cool completely.
Cut egg roll wrappers in half. Have ready a small bowl of cold water and a pastry brush. Working with wrappers one at a time, lay each out so short side of rectangle faces you. Place about 1 Tbsp. filling toward bottom of wrapper. Pull bottom of wrapper over filling, then fold side corners over filling and roll up tightly, like a burrito. Brush far edge with cold water before closing. Continue with remaining wrappers and filling.
Heat 2 cups oil in a large skillet to 350°F. Put a few egg rolls in skillet (don't allow them to touch) and cook, turning over once or twice with tongs, until golden brown, 4 to 5 minutes. Remove with a slotted spoon and drain on paper towels. Allow to cool slightly before serving.