Preheat the oven to 425°F.
Warm the sesame oil in a large wok or nonstick pan over medium-high heat. Wait a minute or two for the pan and oil to heat, then add the onions and garlic. Sauté for a few minutes, or until the onions begin to soften. Add the carrots, asparagus, and mushrooms, and mix together. Cook the vegetables until they just start to soften, 3 to 4 more minutes. Add the peas and scallions. Season the vegetable mixture with salt, pepper, and the soy sauce. Taste and adjust any seasonings as needed. Cook until the vegetables become soft, 2 to 3 more minutes. Add a teaspoon of sesame seeds and a few pinches of crushed red pepper, if desired. Toss together one last time, then remove from the heat and set aside to cool slightly.
To assemble the wontons, set up a work station with a small bowl of water close by. Fill one wonton wrap with about a tablespoon of the veggie filling and top with a 1/2 teaspoon of cream cheese; feel free to use a little more if desired.
To fold the wontons, dip your fingers in the water and wet one corner of the wonton skin wrapper. Pinch this corner together with the opposite corner, over the filling. Wet the other two corners and connect/tuck them into the middle. Press the corners together firmly. This should create a "pillow" shape.
Repeat with filling and shaping the remaining wonton wrappers. Transfer all the wontons to a baking sheet lined with a Silpat or parchment. Brush the wontons with egg wash and sprinkle with sesame seeds and/or furikake. Bake for 10 minutes or until crispy and golden brown.
Remove the wontons from the oven and allow to cool slightly before garnishing with more furikake and the dried seaweed (gim). Serve with dipping sauce. I like a mix of soy sauce with a splash of brown rice vinegar. You can also add some gochugaru for some heat if desired.