Preheat the oven to 350 degrees F.
Place the crabmeat in a bowl and season, to taste, with salt and pepper. Add the green onions and toss gently to combine. Cover and refrigerate.
Spread the almonds on a small baking sheet and toast until golden brown, about 15 minutes. Remove from oven and allow to cool.
Place the tortillas on a work surface. Spread 1/4 cup of the crabmeat mixture evenly over half of each tortilla. Place 5 to 6 slices of the Brie on top of the crabmeat. Fold the remaining half of the tortilla over, forming a half-moon shape. Heat 2 tablespoons of the oil in a large griddle or skillet over medium heat. When smoking hot, carefully lay the quesadilla in the oil. Fry on 1 side until golden brown, about 2 minutes, turn with a spatula and cook until golden brown on the second side and the cheese is melted, 1 to 2 minutes. Remove and repeat with the remaining quesadillas, adding more oil as needed. To serve, cut each quesadilla into 4 triangles.
Spread 1/4 cup of the Chile-Apple Glaze on each plate, and top with quesadilla quarters. Garnish with the toasted almonds and chopped chives.
Yield: 2 to 4 servings