In a frying pan, sauté mushrooms, ginger, garlic, and green onions in about one tablespoon oil.

Once it’s almost done cooking, add soy sauce to deglaze the pan and mix to incorporate. Remove from heat and allow to cool.

Mix mushroom mixture with minced meat and sesame oil. 

In a separate small bowl, mix cornstarch with about two tablespoons warm water to form a paste. Set aside.

Spread out about 10 wonton wrappers on your work surface.

Place one heaping teaspoon of meat mixture into each wonton wrapper.

Dip your finger into cornstarch mixture and spread around perimeter of wonton.

Fold into hamentaschen shape, making sure to close tightly and to push down on filling, to avoid air pockets. (I found that it worked best if once I spread the cornstarch mixture, I folded that dumpling right away).

Heat about one tablespoon oil over medium-high heat in a frying pan (that has a lid). Add about 10 dumplings to the pan. Cook for two minutes without moving the dumplings so they brown.

Reduce heat to medium-low, pour in 1/4 cup water and cover. Cook for an additional three minutes.

While those dumplings are cooking, assemble your next batch. Cook as described above when ready, making sure to remove any remaining water from the previous batch from the pan.

To make peanut sauce, just mix all ingredients together well. To serve, warm dumplings but do not warm sauce.