Place the avocado, onion, jalapeno, garlic, lime juice, salt, and cumin in a large bowl. Using the back of a fork, mash the avocado until smooth and then stir to combine.
Fold the pomegranate arils and cilantro into the avocado mixture. Cover the guacamole and transfer to the fridge until ready to serve.
For the Green Onion Salad
Separate the greens from the whites of each scallion. Thinly slice the white parts and cut the greens into thin ribbons. Place the scallions in a large bowl and cover completely with ice water. Let stand for 10 minutes.
Drain the green onion and place them in a large bowl. Add the remaining ingredients and toss to coat. Cover and refrigerate until ready to serve.
For the Quesadillas
Scatter a small amount of the gouda over one half of a whole wheat tortilla. Layer ham slices on top of the cheese followed by kimchi. Place 4 jalapeno rings on top of the kimchi and add another sprinkling of cheese. Top the whole lot with a small amount of the Green onion salad and fold the naked half of the tortilla on top of the fillings. Repeat with the remaining tortillas.
Pour the olive oil into a large cast-iron skillet. Heat the skillet over medium heat until the oil is shimmering. Add one to two quesadillas to the pan and reduce the heat to medium-low. Fry the quesadillas until both sides are crispy and golden, about 3 minutes per side.
Transfer the finished quesadillas to a cutting board and cut them in half. Arrange the pieces on a platter and serve immediately with a side of pomegranate guacamole.