Sauté onion and sausage in hot oil in a 3-quart saucepan over medium-high heat until tender. Add chicken broth and half-and-half; bring to a boil. Gradually stir in grits and salt. Cover, reduce heat, and simmer, stirring occasionally, 10 minutes or until thickened.
Pour grits onto a lightly greased baking sheet into a 10 1/2-inch circle (should be about 1/3-inch thick); cover and chill 8 hours.
Invert grits circle onto a flat surface; cut into 8 wedges. Brush top and bottom of each wedge with melted butter.
Grill, uncovered, over medium heat (about 300° to 350°) 3 to 4 minutes on each side. Remove and keep warm.
Note: Grits may be broiled, if desired. Prepare as directed, and arrange buttered wedges on baking sheet. Broil 6 inches from heat 2 minutes on each side or until golden.