Place the figs and port in a small saucepan and bring to a simmer over medium-low heat. Cook until the figs have absorbed the port and are plump and tender, 15 to 20 minutes. Remove from the heat and allow to cool.
Prepare the crostini
Preheat oven to 375° F and line a baking sheet with parchment.
Trim the ends from the baguette and slice it on the bias into oval slices about 1/4 to 3/8" thick. You'll need 24 pieces for this recipe.
Arrange the slices in a single layer on the baking sheet. Brush each slice of bread with a little olive oil and bake until lightly toasted and crisp around the edges, about 4 to 6 minutes. Set aside to cool.
Whip the ricotta
Place the ricotta cheese and heavy cream in a mixing bowl, and using a hand-held mixer, whip until smooth and creamy.
Add the toppings
Spread about 2 teaspoons of ricotta on each crostini, then fold a piece of prosciutto on top.
Top with a small spoonful of the figs and press down lightly. Arrange on a serving platter and serve.
Notes
Make-Ahead Tips
The crostini, whipped ricotta, and fig-port compote can be made up to two days in advance. The prosciutto can be sliced ahead as well. For the best flavor, all the ingredients should be brought to room temperature before assembling the finished crostini.
Before storing the crostini, be sure the slices are fully cooled. Place them in a tightly sealed container in a cool dry place. They can also be refrigerated.
The whipped ricotta can benefit from a little whisking once it comes to room temperature.
The fig-port compote will solidify somewhat in the refrigerator. Stir it before topping the crostini.