Preparation Mix first 6 ingredients in medium bowl to blend. Season cheese mixture to taste with salt and pepper. (Can be made 1 day ahead. Cover and chill. Bring to room temperature before continuing.) Mix crabmeat, tomatoes, green onions and chili in large bowl. Spread cheese mixture over half of each tortilla. Spoon crabmeat mixture atop cheese mixture, dividing equally. Sprinkle with salt and pepper. Fold tortillas in half. Press gently to seal. Heat 1 1/2 tablespoons oil in each of 2 heavy large skillets over medium heat. Working in batches, cook quesadillas in skillets until cheese melts and tortillas are golden brown, adding more oil as needed, about 3 minutes per side. Cut quesadillas into wedges and serve.
Preparation Mix first 6 ingredients in medium bowl to blend. Season cheese mixture to taste with salt and pepper. (Can be made 1 day ahead. Cover and chill. Bring to room temperature before continuing.) Mix crabmeat, tomatoes, green onions and chili in large bowl. Spread cheese mixture over half of each tortilla. Spoon crabmeat mixture atop cheese mixture, dividing equally. Sprinkle with salt and pepper. Fold tortillas in half. Press gently to seal. Heat 1 1/2 tablespoons oil in each of 2 heavy large skillets over medium heat. Working in batches, cook quesadillas in skillets until cheese melts and tortillas are golden brown, adding more oil as needed, about 3 minutes per side. Cut quesadillas into wedges and serve.