In a large skillet, heat the oil over medium-high heat. Add 1 1/2 cups red peppers, the green peppers, onion, cumin, and cayenne pepper. Cook until the vegetables are tender, but still firm, about 7 to 8 minutes. Remove from the heat and cool.
In a medium bowl, mix the lobster meat, cheese, jalapenos, salt, and cooled pepper mixture. Divide the mixture into 6 portions. Sandwich each portion between 2 tortillas, spreading the lobster mixture evenly.
Heat a grill or large skillet over medium heat and film the bottom with some of the butter. Place as many quesadillas as will fit without touching, and cook each side until the tortillas are golden brown and the cheese has melted, about 5 minutes. Repeat with remaining butter and quesadillas.
In a medium bowl, combine all ingredients and mix well. Refrigerate for 45 minutes to 1 hour before serving.
Yield: about 3 cups