Preheat oven to 400 degrees F.
In a saute pan, brown the butter with 1 1/2 cups of the figs and the sugar. Season the mixture with salt and pepper. Remove from the heat and pour into a food processor with a metal blade. Puree the mixture for 1 minute. Add the vinegar and process for 30 seconds. With the machine running, slowly add the vegetable oil until the dressing is emulsified. Season the dressing with salt and pepper. Fold in the reserved figs. Pour the dressing into a saucepan and warm the dressing.
Remove the crust from the brioche and cut into 1/2-inch cubes. In a medium mixing bowl, toss the croutons with the olive oil. Season with salt and pepper. Place on baking sheet and bake until golden, about 8 to 10 minutes. Remove, cool and set aside.
In a large mixing bowl, toss the greens with desired amount of the dressing. Mound the greens in the center of each plate. Arrange the quartered figs, ham, and croutons around the greens. Crumble the cheese on top of the greens. Garnish the salad with cracked pepper around the rim of the plate.