Preheat oven to 190 degrees C. Line two baking trays with baking paper.
Melt the butter and olive oil in a large frypan over medium heat. Stir the onions into the butter and cook until the onions have softened and caramelized to a deep, golden brown, 30 to 40 minutes. Stir frequently as the onions cook to keep them from burning. Once done, season with salt and pepper and set aside to cool.
Use a sharp knife to cut each sheet of puff pastry into 9 squares. Cut each square in half diagonally to yield 36 triangles. Place the triangles onto the prepared baking trays, and top with the caramelized onions, pears, and 1 teaspoon of blue cheese.
Bake in the preheated oven until the pastry is puffed and golden brown, 20 to 30 minutes. Allow to cool to room temperature before serving.