4 cups water
1 1/4 teaspoons salt
1 tablespoon minced fresh sage leaves or 1 teaspoon dried, crumbled
1 1/3 cups yellow cornmeal
1/2 stick (1/4 cup) unsalted butter
1 cup freshly grated Parmesan cheese (about 1/4 pound)
Butter a 13- by 9-inch glass baking dish. In a large heavy saucepan bring water to a boil and add salt. Add sage and 1/3 cup cornmeal., a little at a time, stirring constantly. Reduce heat to low and add remaining cup cornmeal in a slow stream, stirring constantly. Cook mixture over low heat, whisking, 1 minute and remove pan from heat. Add 2 tablespoons butter and 1/3 cup Parmesan and stir polenta until butter is incorporated.
Working quickly, spread polenta evenly in prepared dish and chill until firm, about 20 minutes. Polenta may be prepared up to this point 1 day ahead and chilled, covered.
Preheat broiler and line a baking sheet with foil. In a small saucepan melt remaining 2 tablespoons butter over low heat. Invert polenta onto a work surface.
Halve polenta lengthwise and cut each half crosswise into 14 sticks. Arrange sticks on prepared baking sheet and brush with melted butter.
Broil sticks about 4 inches from heat until golden, about 4 to 6 minutes.
Turn sticks over and sprinkle with remaining Parmesan. Broil sticks until cheese is golden, about 2 to 3 minutes more.