Bring chicken stock or water and milk to a boil in a large saucepan over high heat.
Add cornmeal in a steady, gradual stream, whisking continuously to prevent lumps; boil for 1 to 2 minutes.
Reduce heat to low and whisk almost continuously for about 30 minutes, or until the mixture begins to thicken considerably.
Stir in paprika, salt, pepper, and 2 tablespoons of 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.
Remove chilled polenta from baking pan and cut into squares or right-angled triangles.
In a small, grill-safe saucepan, melt the remaining teaspoon of butter, add polenta, and grill over direct medium-high heat for about 4 to 5 minutes on each side, or until lightly browned.
Serve with sweet-rubbed ribeyes.