Put berries, wine, and sugar in a medium saucepan and coarsely mash with a potato masher. Bring mixture to a boil over medium-high heat. Reduce heat and simmer, stirring often, until reduced to 2/3 cup, 10 to 20 minutes. Add pepper to taste. Let cool to room temperature, about 25 minutes.
Spoon compote into a small bowl. Set on a board alongside cheese, basil, a pepper grinder, and crackers for guests to serve themselves.
Make ahead: Through step 1, up to 3 days, chilled.