Step 1Put the figs and wine in a small saucepan, bring to a boil and simmer, stirring constantly, until most of the Port has reduced, 5 to 6 minutes. Remove from the heat and reserve.
Step 2Remove the rind from the Brie; you should have about 8 ounces left. Put the cold cheese into a mixer with a paddle attachment and beat at medium speed, scraping down the sides from time to time, for about 10 minutes, until the cheese is very white and creamy. Beat in the pepper.
Step 3Add 1 tablespoon oil to a large skillet and heat over medium heat. Drizzle about one-eighth teaspoon of balsamic vinegar over each slice of baguette in a thin line, brush lightly with oil on both sides and cook each side until golden brown, about 2 minutes. Brown the bread in batches. Remove from the heat and reserve. (The bread can be stored in a plastic bag or container until needed.)
Step 4For each serving put a crouton on the plate, then angle a quenelle of Brie over the crouton. Top with a second crouton and another quenelle of Brie, then another crouton. Place about a tablespoon of the fig compote and a sprinkle of fleur de sel next to the stack and serve immediately. Repeat for six plates total.