For polenta, in a 3-quart saucepan bring the 3 cups water to boiling. In a medium mixing bowl combine cornmeal, the 1-1/2 cups cold water, and the 1 teaspoon salt. Slowly add cornmeal mixture to boiling water, stirring constantly. Cook and stir until mixture returns to boiling. Reduce heat to very low. Cover and simmer for 15 minutes, stirring occasionally. Stir 3/4 cup of the shredded cheese into hot polenta. Turn the hot mixture into an ungreased 13x9x2-inch pan. Cool slightly. Cover and chill in the refrigerator at least 6 hours or until firm.
Meanwhile, for sauce, place pepper halves, cut side down, on a foil-lined baking sheet. Bake in a 425 degree F. oven for 20 to 25 minutes or until skin is brown. Wrap in the foil and let cool so the steam loosens the skins.
When peppers are cool enough to handle, peel off skins, using a sharp knife. In a blender container combine peeled peppers, sugar, vinegar, and salt. Cover and blend until smooth. Transfer to a small saucepan; heat through.
Cut the chilled polenta into 18 triangles. Arrange the triangles on a lightly greased baking sheet. Brush with olive oil. Broil 4 to 5 inches from heat for 4 minutes. Turn over triangles. Brush with more oil. Broil for 4 minutes more or until golden brown. Sprinkle remaining 3/4 cup cheese over polenta. Let stand for 2 minutes or until cheese is melted.
To serve, arrange polenta triangles on plates lined with arugula leaves, if desired. Top with warm pepper sauce. Makes 9 side-dish servings.