Heat 1 tablespoon olive oil in a skillet over medium heat. Cook pork until until slightly pink in the center, 5 to 7 minutes. Remove from heat and allow to cool. Chop into small chunks.
Combine cabbage, spring onions, garlic, and ginger in a food processor. Blend until finely minced; transfer to a bowl.
Place cooked pork in the food processor; blend until finely minced. Add pork, soy sauce, sesame oil, salt, and pepper to the cabbage mixture. Combine filling well.
Separate and place gyoza wrappers onto your work surface. Spoon about 1 tablespoon of the filling onto the center of each wrapper. Use your finger or a pastry brush to lightly moisten edges of wrappers with water. Fold one side of the wrapper over the filling onto the opposite corner to form a crescent shape. Press edges together to seal.
Heat olive oil in a skillet over medium heat. Fry gyoza until bottoms are golden, about 3 minutes. Add enough hot water to cover gyoza halfway. Cook until water is evaporated and gyoza are translucent, 2 to 4 minutes.