Preheat the oven to 400˚F. Line a baking tray with parchment paper and set aside.
Working on a large, clean surface, unroll the phyllo sheets. Place 1 sheet in front of you, landscape orientation, and using a pastry brush, lightly coat all over with melted butter. (Keep the remaining phyllo sheets covered by a tea towel while you work to keep them from drying out). Place another phyllo sheet on top of the first and coat with more butter. Using a sharp knife or pizza wheel cutter, cut the layered sheets into 3 even vertical strips. Repeat this process with the remaining two sheets of phyllo dough.
Cut the brie into 6 small rectangles (approximately 1 x 2-inches each) and place the first horizontally at the bottom of one of the strips of phyllo. Spread ½ teaspoon of the jam on top of the brie. Roll the brie once in the pastry and then fold in the edges of the pastry and continue to roll until you have used the whole strip. (The brie and jam should be completely enclosed in the phyllo). Place on the prepared baking tray. Repeat this step with the remaining 5 strips of phyllo.
Brush each prepared roll-up with more melted butter and sprinkle with sesame seeds, if desired. Bake in the oven for 12 – 15 minutes, or until golden. (The jam and brie get a bit oozy when they heat so you may also see some starting to seep out).
In a small pot over low heat (or in the microwave), warm the remaining 3 tablespoons of jam. Arrange the roll-ups on a platter and serve the warm jam on the side for dipping.
Cook’s tip: If you are making this for a larger group, just continue pulling out 2 phyllo sheets at a time (making sure to keep the rest covered while you work) and repeat the steps above.