Preheat oven to 350 degrees F with rack in middle position. Line a baking sheet with parchment.
Cut rind from Brie and discard. Cut Brie into 24, 3/4-inch cubes. Stack prosciutto slices, roll, and slice into 1/4-inch thick ribbons.
Place phyllo shells on prepared baking sheet. Fill each shell with 1/2 teaspoon fig jam, spreading gently. Add one Brie cube to each shell and top with a few pieces of cut prosciutto.
Bake 8-10 minutes, until cheese is melted and prosciutto is crisp.
While the shells are baking, cut each fig into 8 pieces (cut fig in half, and then cut each half in half lengthwise and crosswise, creating 4 pieces per half).
Remove phyllo cups from the oven and top with a piece of fresh fig. Serve warm.
Ready-to-fill phyllo shells are available in most grocery store freezer cases, located by the phyllo sheets, pie crusts, and puff pastry. I buy them in trays of 12 to 15.If fresh figs are out of season, omit, or top with dried figs that have been steeped in boiling water for 10-15 minutes. Drain figs from water, pat dry, and cut into bite-sized pieces.
Fully assemble the Brie Bites and store, covered, in the refrigerator for up to one day before baking as directed and serving.