"This is definitely an acquired taste. There aren't many people who can take the habanero-wasabi combo, but those who can love this. I've made toned-down versions with less intense peppers for the faint of heart as well."
Combine soy sauce, sugar, ginger, and garlic in a large bowl. Add chicken strips; toss to coat. Cover with plastic wrap and let marinate in the refrigerator, at least 1 hour.
Preheat oven to 425 degrees F (220 degrees C). Transfer chicken strips to a glass baking dish; discard marinade.
Bake chicken strips in the preheated oven until no longer pink in the center and an instant-read thermometer inserted into the center reads at least 165 degrees F (74 degrees C), about 20 minutes.
Brush both sides of 1 tortilla with olive oil and lay on a flat surface. Sprinkle 1/3 of the pepperjack cheese on top. Add 1/3 of the chicken strips. Cover chicken with 1/3 of the Parmesan cheese. Add 1/3 of the chopped habanero and 1 teaspoon wasabi paste. Brush both sides of a second tortilla with olive oil and place on top. Repeat with remaining ingredients to make 2 more quesadillas.
Heat a lightly oiled griddle over medium-high heat. Cook quesadillas until browned and cheese is melted, about 3 minutes per side.