Dry tofu by placing it on paper towels on a plate. Place more paper towels on top and cover with another plate. Top with cans and let it press the tofu for 20 to 30 minutes.
For the Filling: Meanwhile heat 2 tablespoons avocado oil over medium heat in a large sauté pan. Add garlic and ginger, and cook for 1 minute, stirring. Add mushrooms, cabbage, carrots, and scallions, and continue cooking until cabbage has softened, 4 to 5 minutes. Crumble drained tofu into vegetables. Add soy sauce, oyster sauce, Sriracha, and sesame oil. Cook, stirring frequently, until moisture has evaporated from the bottom of the pan, 1 to 2 minutes. Remove from head and stir in the POM Arils. Let mixture cool.
For the Dipping Sauce: In a small bowl, whisk together the soy sauce, POM Juice, rice vinegar, and sesame oil. Stir in the garlic and set aside.
For the Pot Stickers: Place about a tablespoon of filling into the center of each dumpling wrapper. Dip your fingertip in water and wipe around the edge of the wrapper. Fold in half and pleat the edge to seal. Place on a parchment-lined baking sheet. To keep the pot stickers from drying out keep them covered with a damp paper towel. Continue making pot stickers until all the filling is used or refrigerate leftover filling for up to 3 days.
To cook the pot stickers, heat ½ tablespoon avocado oil in a skillet with a lid over medium heat. Place 8 pot stickers into the pan once it's hot, make sure they aren't touching. Fry pot stickers until bottoms are just starting to turn golden, 2 to 3 minutes. Add 2 tablespoons water to pan and immediately cover with the lid. Steam 3 to 4 minutes until pot stickers are soft and dumplings are heated through. Remove cover, making sure not to get any steam water back into the pan and continue to cook up to 1 more minute until all water is evaporated.
Serve pot stickers immediately with the dipping sauce, garnished with sesame seeds and POM Arils.