In a large bowl, mix together ground pork, minced shiitake mushrooms, green onions, soy sauce, sesame oil, cornstarch, salt, pepper, ginger, and garlic until well combined.
Place one wonton wrapper on a clean surface and brush the edges with water.
Spoon 3/4 teaspoon of filling onto the center of the wrapper.
Fold the wrapper into a triangle, then pinch the corners together to form a purse shape, making certain all edges are sealed.
Repeat with remaining wrappers and filling.
Heat 3 inches of vegetable oil in a deep pot or fryer to 375°F.
Deep-fry wontons in batches until golden brown and crispy, about 2-3 minutes per batch.
Remove with a slotted spoon and drain on paper towels.
Serve immediately with sweet chili sauce if desired.