Preheat the oven to 350°F(180°C). Arrange the baguette slices on a baking sheet and brush lightly with the oil. Bake until crisp and golden, 10–15 minutes. Transfer to a large platter.
Cook the pear compote
In a frying pan over medium-low heat, combine the pears, star anise, wine, and sugar. Bring to a gentle simmer and cook, stirring occasionally, until the pears are softened, about 12 minutes. Remove the star anise. Let cool to room temperature. (The compote may be refrigerated for up to 8 hours; bring it to room temperature before serving.)
Arrange the platter
Transfer the compote to a small bowl and place on the platter. Arrange the cheeses and crostini around the compote. Layer a slice of cheese and a dollop of compote on each crostini and serve.