Preheat the oven to 350°. Line a large baking sheet with parchment paper and set aside.
In a small saucepan, heat two tablespoons of the butter over medium high heat, until it begins to foam. Add the diced pears and shallots and cook for 2 minutes, stirring occasionally until tender -- but the pears shouldn't be falling apart. Add the brown sugar and vinegar and cook for an additional 3-5 minutes until syrupy (don't over stir -- you want the pears to retain some shape). Remove from heat and let pear mixture cool.
Cut the rind from the brie and dice the cheese into 1 inch cubes. Wrap the brie chunks with prosciutto and set aside.
Place the remaining 4 tablespoons of butter in a small bowl, cover with plastic wrap and microwave in 15 second increments until melted.
Cover your work surface in plastic wrap (this is optional, but it makes cleanup a lot easier). Place one sheet of phyllo dough on the work surface. Use a pastry brush to spread melted butter along one half (lengthwise) of the phyllo dough. Fold the dry portion of the dough over on itself and pat to seal. Place a brie and prosciutto bundle in the lower right corner of the phyllo (leaving about 1" edge on either side". Spoon a portion of pear compost over the brie and prosciutto. Brush the edges of the phyllo surrounding the brie with butter and fold the pastry diagonally over the filling to form a rectangle. Continue to brush the top of the wrap with butter and continue folding over and back until the pocket is completely sealed. Brush with extra butter and place on the cookie sheet.