To prepare the polenta, bring the stock and milk to a boil in a large saucepan over high heat. Add the cornmeal in a steady, gradual stream, whisking continuously to prevent lumps. Boil for 1 to 2 minutes. Turn down the heat to low and whisk almost continuously for about 30 minutes, or until the mixture begins to thicken considerably. Stir in the paprika, salt, pepper, and 2 tablespoons of the butter, and transfer to a greased 9-inch square baking pan, spreading with a spatula to make an even layer. Let chill in the refrigerator for 4 hours or overnight, until firm.
To prepare the rub, combine the sugar, pepper, paprika, cumin, and salt on a platter and coat the steaks with the mixture. Let sit in the refrigerator for 30 minutes, then bring to room temperature.
Turn out the chilled polenta and cut into squares or right-angled triangles. In a small saucepan, melt the remaining teaspoon of butter (or substitute 1 teaspoon olive oil), brush on the polenta, and grill over direct medium-high heat for about 4 to 5 minutes on each side, or until lightly browned.
Grill the steaks over direct medium-high heat to desired doneness. Serve with the polenta.