Heat 1 teaspoon of the canola oil in a skillet over medium heat. Add the onion and bell pepper and sauté until soft, 4 to 5 minutes. Transfer the vegetables to a bowl.
Add the remaining 1 teaspoon oil to the skillet and raise the heat to medium-high. Add the chicken to the skillet. Season with the salt and pepper. Cook the chicken until brown, 5 to 7 minutes. Stir, breaking up the chicken into smaller pieces. Transfer the cooked chicken to the bowl of onion and bell pepper. Toss to evenly distribute and then refrigerate until cool. When the ingredients are cool, stir in the Velveeta.
Clip a deep-frying thermometer to the side of a heavy deep pot. Add 2 inches canola oil to the pot and slowly heat the oil to 350°F.
To assemble the egg rolls, position 1 wrapper on a work surface like a diamond. Place 2½ tablespoons filling close to the corner nearest you and spread it up toward the middle. Using a pastry brush, brush the edges with a little water. Fold the corner closest to you up over the mixture, fold the left and right corners toward the center, and continue to roll. Brush the final corner with water to help seal the egg roll. (The egg rolls can be frozen for up to 1 month before frying.)
Using a slotted spoon, lower 4 egg rolls into the hot oil and cook until golden brown, 3 to 5 minutes, turning them halfway while frying. Transfer the cooked egg rolls to a paper towel–lined plate to drain. Fry the remaining egg rolls and serve hot.