Prepare the figs by washing and removing the stems. Depending on the size cut into quarters or halves. Make a slit down the side of each fig to make a pocket.
In a bowl, mix the cream cheese, goat cheese, and basil together then take half of the cheese mixture and stuff the figs by pressing a little into each pocket.
Make a slit in each date and use the remainder of the cheese mixture to fill each date.
Preheat the oven to 180 degrees C.
Wrap the figs and dates with the prosciutto. The prosciutto will usually stick to itself when wrapping but if not you can use a toothpick to hold it together. Brush the figs and dates lightly with olive oil and place on a baking tray. Season with salt and pepper.
Bake in the oven for about 10 minutes. Watch closely to make sure they don't burn. You want to warm the figs and dates and lightly crisp the prosciutto.
Meanwhile, combine the balsamic vinegar and maple syrup in a saucepan over a medium heat and stir frequently. Continue cooking until the mixture reduces down to a consistency that coats a spoon and allows you to drizzle it over the figs and dates. The reduction will become more firm as it cools.
Remove the figs and dates from the oven and place on a serving platter. Drizzle with the balsamic reduction and serve.