In a bowl, add the soy sauce, the peanut butter, the black pepper, the onion powder, and the garlic powder and whisk to combine. Set the soy sauce mixture aside.
In a separate bowl, add the rice wine vinegar, the green parts of the green onions, and the ginger and whisk to combine. Set the vinegar mixture aside.
In a skillet over medium-high heat, add the neutral-flavored oil.
Add the ground pork to the hot oil and cook, while crumbling, until it is cooked through, about 5-7 minutes.
Add the white parts of the green onions and cook, while stirring, until softened, about 5 minutes.
Add the soy sauce mixture to the pork mixture and stir to combine.
Reduce the stovetop heat to low and allow the pork mixture to simmer until the flavors meld together, about 15 minutes.
Add the cabbage to the vinegar mixture and toss to combine.
Turn off the stovetop heat.
Add the cabbage mixture to the pork mixture and toss to combine.
Allow the pork mixture to rest until slightly cooled.
Place a strainer over a bowl.
Transfer the pork mixture into the strainer and allow it to sit until the excess liquids fully drain out, about 30 minutes.
Pour the water into a small bowl.
Set up a work surface with the bowl of water, a wooden cutting board, a cookie sheet lined with parchment paper, and some damp towels to clean your hands, as needed.
Place 1 of the egg roll wrappers in front of you on the wooden cutting board with one of the corners facing down.
Spoon 3 heaping tablespoons of the pork mixture down the center of the wrapper, making sure that the pork mixture does not touch the edges of the wrapper. Aim to have at least a 1/2-1-inch border on all sides.
Fold the bottom corner closest to you over the filling, tucking it slightly underneath the pork mixture. Tightly fold the left and right sides of the wrapper inwards over the bottom corner and the pork mixture. Lightly brush the top of the wrapper with the water to seal. Starting from the bottom, roll the egg roll up tightly, ensuring the edges are sealed with more of the water, as needed.
Transfer the prepared egg roll to the prepared cookie sheet and repeat until all of the egg rolls are filled and rolled.
Transfer the egg rolls on the cookie sheet to the refrigerator and let them chill until hardened slightly, about 1 hour.
In a deep skillet over medium-high heat, add about 2-inches of the neutral-flavored oil until it reaches 350 degrees F.
Add the egg rolls in batches to avoid cooling the oil too much and cook, while carefully turning the egg rolls as needed, until they are golden and cooked through, about 3-5 minutes.
Transfer the egg rolls to paper towels to drain and repeat until all of the egg rolls are cooked. Make sure to allow the oil to return to temperature before adding the next batch.
Serve hot.