Heat 1/2 tablespoon of olive oil in a large skillet over medium-high heat. Once hot, add the kimchi. Cook for 5-6 minutes, stirring occasionally, until the kimchi starts to soften and brown in spots. (You can deglaze the pan with a splash of water if needed.)
While the kimchi caramelizes, add the sauce ingredients to a food processor or blender.
Once the kimchi is ready, add it to the food processor with the sauce ingredients. Set aside.
Add the remaining 1/2 tablespoon of olive oil to the skillet, followed by the ground chicken. Cook one side for 2-3 minutes until golden brown before breaking the chicken apart with a spatula and fully cooking.
While the chicken cooks, blend the kimchi and sauce ingredients together until smooth.
Add the sauce to the cooked ground chicken and cook for 2-3 minutes until the sauce thickens and evenly coats the chicken.
To make the quesadillas, add a bit of cooking spray to a separate pan or griddle. Add a tortilla and top with 2 ounces of shredded mozzarella and 75g of the chicken and kimchi mixture. Fold the tortilla over to seal and cook both sides until golden brown.
Repeat with all 8 tortillas. Serve the quesadillas with the creamy gochujang dip from the notes section below.