Melt 2 1/2 tablespoons of butter in a skillet over medium heat. Saute crimini and shiitake mushrooms with garlic until tender. Remove from heat, and set aside. Melt remaining butter in a dish in the microwave.
Preheat the oven to 375 degrees F (190 degrees C).
Unroll the phyllo dough, and cut into three equal strips, about 3x12 inches. I like to use kitchen shears for this. Place two sheets of the phyllo onto a cutting board or other work surface, and cover the stack of remaining sheets with a damp paper towel to keep them from drying out.
Brush the top sheet of phyllo with melted butter, and place a raspberry sized dab of brie on one end. Top with a small amount of the mushroom mixture. Fold phyllo dough over the filling to make a triangle. Continue folding back and forth in a triangle shape, brushing the exposed side of the dough as you go. Seal the end closed with a little water or butter. Place on an ungreased baking sheet, and repeat with remaining dough and filling.
Bake the triangles for 20 to 25 minutes in the preheated oven, turning over once during baking, until golden brown.