Preheat the oven to 400° F / 204° C. Line a baking sheet with parchment paper and set saide.
To poach the figs, combine the Port and balsamic vinegar in a small sauce pan. Add a pinch of kosher salt and pepper and place over medium heat. Add the dried figs and bring the Port to a simmer.
When the Port comes to a simmer, take off the heat and cover with a lid. Let the figs steep for 15 minutes to soften. Then transfer the figs to a paper towel lined plate to drain and cool off.
Turn the heat back up to medium high and bring the Port to a boil. Continue boiling the Port until it has reduced down to a thick glaze. This should take about 5 to 10 minutes and yield approximately 3 tablespoons of glaze. If the glaze becomes too thick you can add a few drops of Port wine to thin it out. Set the glaze aside.
To wrap the figs, cut a deep slit lengthwise down the side of each fig. Gently widen the cut to create a small pocket. Stuff the figs with a teaspoon or so of the soft goat cheese. Cut each slice of prosciutto in half lengthwise. Wrap each fig with a strip of prosciutto, taking care to cover the cut side well. For a decorative look, twist the strip of prosciutto on the last wrap around the fig.
Place the wrapped figs on the parchment lined baking sheet, spacing them apart. Bake for 10 to 15 minutes until the figs are heated through and the prosciutto begins to brown on the edges and bottom.
The glaze will have thickened while it cooled. Reheat the glaze on the stove or in the microwave to make it pourable. Add a splash of Port wine if the glaze is too thick.
To serve, transfer the warm figs to a platter. Drizzle with the Port glaze and enjoy!