Prepare the shrimp by roughly chopping them into pea-sized pieces. Heat sesame oil in a large skillet or wok over medium-high heat. Add the minced garlic and ginger, stirring constantly for 30 seconds until fragrant.

Add the chopped shrimp to the skillet and cook, stirring, for 1-2 minutes until just pink and opaque. Add the coleslaw mix and sliced green onions, and continue to cook for another 2-3 minutes until the cabbage has slightly wilted but remains crisp-tender.

In a small bowl, whisk together the soy sauce, rice vinegar, and cornstarch until smooth. Pour this slurry over the filling in the skillet and stir continuously until the sauce thickens and coats all ingredients. Remove from heat.

Transfer the filling to a baking sheet and spread it in a thin layer to cool completely. To speed this up, place it in the refrigerator or freezer for 15-20 minutes. This step is crucial to prevent soggy egg rolls.

Place an egg roll wrapper on a clean surface in a diamond shape. Spoon 2-3 tablespoons of the cooled filling onto the lower third. Fold the bottom corner over the filling, tucking it in snugly. Fold in the left and right corners like an envelope, then roll it up tightly towards the top corner. Moisten the top corner with water and press to seal. Repeat with remaining filling and wrappers.

Pour 2-3 inches of oil into a heavy-bottomed pot and heat to 350°F (175°C). Carefully fry 3-4 egg rolls at a time for 3-5 minutes, turning occasionally, until deep golden brown and crispy. Do not overcrowd the pot.

Remove the cooked egg rolls with a spider strainer or tongs and let them drain on a wire rack to maintain crispiness. Repeat the frying process with the remaining egg rolls, ensuring the oil temperature returns to 350°F between batches.