Heat a small skillet over medium-high heat, add a small amount of vegetable oil, and sauté the chopped mushrooms until soft. Set aside to cool.
In a mixing bowl, combine the pork, mushrooms, garlic, ginger, green onions, and cornstarch. Season the mixture 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 and fold it into a triangle shape. Bring the two bottom corners together and seal them with a little water.
Heat the vegetable oil for frying in a large deep pot to 375°F. You will need about 2 inches of oil in the pot. Work in batches if necessary; do not overcrowd the pot.
Fry the filled wontons in the hot oil for 4-5 minutes until golden brown. Drain on a paper towel and top with sesame seeds.
Serve the fried wontons hot with the sauce of your choice.