In a small saucepan, combine the Marsala and salt and bring to a boil. Simmer over moderate heat until reduced by one-third, about 4 minutes. Let cool to room temperature.
In a large bowl, gently mix the pork with the Marsala, sage, pepper and pimentón until evenly seasoned. Shape the meat into 8 thick burgers.
Light the grill. Lightly brush the burgers on both sides with olive oil and grill over a moderately hot fire for about 6 minutes per side, or until nicely browned outside and barely pink inside. Serve hot, on the hamburger buns.
Pimenton, a smoked Spanish paprika, is available at specialty markets.