Bring the ham hocks and 3 quarts water to a boil in a large saucepan over high heat. Reduce the heat to medium-low. Simmer, uncovered, until the meat is very tender, about 2 hours. Drain the ham hocks and let cool until easy to handle.
Remove the meat from the bones, discard the skin and bones, and coarsely chop the meat. Blend the meat and goat cheese in a large mixing bowl with a fork. Stir in the green onions, olive oil, parsley, garlic, salt, and pepper.
Lay 12 of the wonton skins on a work surface; have a cup of water at hand. Put a generous teaspoon of the meat mixture in the middle of each skin. Rub a bit of water along the edges of each skin and fold in half to make a triangle, pressing down the edges to seal. Transfer to a cornstarch-dusted baking sheet. Repeat with the remaining skins and meat mixture. (The filled wontons can be covered tightly with plastic wrap and refrigerated for up to 2 hours before frying.)
Pour enough oil to come halfway up the sides of a large heavy pot or electric deep fryer, and heat over high heat to 360°F. In batches, without crowding, deep-fry the wontons, stirring occasionally, until they float to the top and are golden brown, about 3 minutes. Using a slotted spoon, transfer to paper towels to drain.
Serve immediately, with the dipping sauce of your choice.
Yield: 6 servings