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.

In a small saucepan, combine the apples, vinegar, sugar, shallots, jalapeno, and garlic. Bring to a boil over medium-high heat. Reduce the heat to medium-low and simmer until the apples are translucent and soft and the vinegar has reduced by half, about 15 minutes. Remove from the heat and cool for at least 10 minutes. Once cool, transfer to a blender or food processor and puree until smooth, about 1 minute. Season to taste with salt and pepper.