Prep figs. Use a paring knife to cut off any bits of stem that may remain on the dried figs. Then make a slit with the knife in each fig -- the slits should be made lengthwise and go about halfway through. Set aside.
Hydrate figs. Pour the port into a small saucepan and add the figs. Gently stir to be sure they're well coated, and to a bring boil. Turn the heat off, cover, and let the figs hydrate for about 30 minutes.
Prep cheese. While the figs are hydrating, remove the rind from the Manchego and cut it into 2 dozen tiny chunks that will fit snugly into the slits in the figs.
Preheat the broiler and line a sheet pan with parchment paper.
Assemble. Use a slotted spoon to remove the figs from the port (save what's in the saucepan!), placing them directly on the parchment-lined sheet pan as you go. Very gently squeeze a chunk of Manchego into each slit in the figs.Then, use your hands to tear thin strips from the prosciutto -- they should be about 2 x ½-inch strips. They might not stay intact, and that's okay. Wrap a strip around each fig. It should wrap around the fig at least once, and twice is also okay. Be sure the "seam" is on the bottom. Make glaze. To make the glaze, bring the port remaining in the saucepan to a strong simmer. Do not cover, and let it simmer for about 5 minutes or so, just until it's a nice, thick consistency. Set aside.
Heat under broiler. Place the sheet pan under the broiler just until the cheese is melted and the prosciutto begins to sizzle or brown.
Glaze and serve. Carefully put them on a platter and stick a small toothpick into each fig. Drizzle generously with the port glaze and serve. (If the glaze has become firm at all, simply warm it again.)