1. Prepare the polenta: Bring the water to a boil in a saucepan. Slowly pour in a continuous stream of cornmeal, stirring constantly. Add the salt. Reduce the heat to low and cook uncovered, stirring occasionally, until the polenta begins to pull away from the sides of the pan, about 20 minutes. Shut off the heat and stir in the basil and cheese. Working quickly, grease with olive oil a medium-size (approximately 9 x 7 inches) shallow casserole dish or pan and pour in the cornmeal, spreading it out over the whole surface. Let the polenta set and cool for 1 hour.
2. Preheat oven to 400° F.
3. Prepare the Roasted Bell Pepper Puree: Cut the sweet red peppers into large pieces. Smear a little of the olive oil over the bottom of an ovenproof casserole dish and lay the peppers inside. Cover and bake for 20 minutes until they become soft. Remove from the oven (leave the oven on to bake the polenta) and let cool. Put the peppers in a food processor and process until smooth. Add the remaining ingredients including all but a teaspoon of the remaining olive oil, and process until thoroughly blended. Scrape the dip into a serving bowl.
3. When the polenta has cooled completely, cut two vertical lines through it, so you have three rectangles. Make diagonal cuts from corner to corner of each rectangle to make an "X," creating 4 triangles within each of the 3 rectangles.
4. Smear some olive oil over a baking sheet and with a spatula remove each of the 12 triangles and arrange them on the sheet, leaving space around each one so that the edges can crisp. Bake on the top rack in oven for 15 minutes, or until browned.
5. To serve, pour 2 tablespoons of the Roasted Bell Pepper Puree on each of 6 serving plates. Arrange 2 Polenta Triangles alongside, sprinkle some chopped parsley and Parmesan over them, and place a basil sprig on the side.
Makes 12 – 2 per person.
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