In a small bowl, stir together peanut dipping sauce ingredients until smooth. Set aside.
In a medium skillet over medium-high heat, sweat the cabbage and carrots with 1 tsp olive oil for approximately 2 minutes, until softened. Add cabbage and carrot mixture to a large bowl.
Stir in cooked ground turkey, jalapeno, basil, soy sauce, garlic power, black pepper, salt, and peanut dipping sauce. Gently fold in chopped avocado.
In a small bowl, whisk together cornstarch and cool water.
To wrap your egg rolls, start with a clean, flat surface. Lay one wrapper so one of the corners is facing you (like a diamond).
Dip your fingers in the cornstarch water and spread on each edge of the egg roll wrapper. In the corner closest to you, spoon 1 to 1 1/2 tablespoon of the filling into the center. Lift the bottom corner up and begin to roll away from you, making sure you tuck the corner under as you roll. Once you are halfway up the wrapper, fold in the left side and then the right side towards the center. Continue rolling away from you until only the final corner is ready to roll.
Dip your fingers in the cornstarch and water mixture you made earlier and brush it over the final corner. Finish the roll, brush a little more of the cornstarch mixture along the seam, and place seam-side down. Make sure you roll the egg rolls tightly. If they are too loose, they will fall apart when you fry them.
Fill a pot with 4-5 inches of cooking oil. Heat the oil to 350°F.
Gently add the egg rolls to the hot oil, frying no more than 3 or 4 at a time, turning occasionally. Fry until the egg rolls are golden brown on all sides, approximately 2 to 3 minutes. Place on paper towels to drain and cool.
Serve immediately with peanut dipping sauce.