Soak the skewers in water to cover for at least 30 minutes.
In a small saucepan over medium heat, melt the butter. When it foams add the shallots and saute until translucent, about 1 minute. Sprinkle with 1/2 teaspoon each of the salt and pepper. Raise the heat to high and add the wine. Cook until reduced by half, about 4 minutes. Add the balsamic vinegar and continue cooking until reduced to about a third, about 4 minutes longer. Remove from the heat and set aside. (If making ahead, let the reduction cool, then cover and refrigerate until ready to use. Add the 1/2 teaspoon butter and reheat gently over medium heat.).
Preheat the broiler. Cut the filet mignon into 1-inch cubes. You should have about 24 cubes. Transfer the cubes to a bowl, pour the reduction over them, and turn to coat. Drain the skewers and thread 3 cubes of beef onto each skewer. Arrange the skewers on a broiler pan, spacing them about 1 inch apart. Season with the remaining 1 teaspoon each sea salt and pepper.
Place in the broiler about 6 inches from the heat source and broil until just browned, about 3 minutes. Turn and broil until just browned on the second side, about 2 minutes for medium-rare or 3 minutes for medium. Transfer to a platter, garnish with the rosemary and serve hot.