Heat a small skillet on medium-high heat, add the oil, and sauté the chopped mushrooms until soft. Set aside and cool down.
In a mixing bowl combine the pork, mushrooms, garlic, ginger, green onions, and cornstarch, and season with the soy sauce, sesame oil, and black pepper. Mix with your hands until well combined.
Place the wonton wrappers on a clean surface and brush the edges with some water. Place a teaspoon of the pork filling into the center of each wonton wrapper.
Fold it into a triangle shape. Bring the two bottom corners together and seal with a little water.