To make polenta, bring water to a boil in a large saucepan. Add salt and reduce the heat to medium low. As soon as water simmers, slowly add cornmeal in a thin stream. Using a wire whisk, stir constantly to avoid lumps. Once all cornmeal has been added, switch to using a wooden spoon. Keep heat at a low simmer. Cook polenta for 25 to 30 minutes. As it cooks, polenta will thicken and bubble. Take care as the hot polenta may splatter out of the pan. Polenta is done when it pulls away easily from the sides of the pan. Remove from the heat and stir in butter, cheese, chili powder and hot sauce.
Butter a 12x17-inch rimmed sheet pan. Pour polenta onto the sheet pan and set aside to firm up. This will take about an hour at room temperature or 30 minutes in the refrigerator.
For chicken, heat olive oil in a sauté pan. Add thinly sliced onion, salt, pepper and sugar. Cook over medium heat, stirring occasionally until well caramelized, about 20 minutes. Stir in barbecue sauce and mix well. Stir in shredded chicken and warm over low heat.
For the avocado sauce, combine avocados, lime juice, garlic, salt, oil and water in a blender. Puree until smooth. Taste and adjust seasoning with salt and lime juice. Transfer mixture to a small bowl and chill until ready to use.
To assemble, use a 2-inch round cutter to cut 40 rounds of polenta. Heat oil in a sauté pan. Working in batches, lightly sear both sides of the polenta rounds, 3 to 5 minutes. Set seared rounds on a baking sheet.
Spread a bit of avocado sauce on each polenta round. Top with a spoonful of chicken. Garnish with a bit of lime zest and a tiny pinch of ancho chili powder. Transfer to a warmed platter and serve immediately.
Yield: about 40 hors d'oeuvres.
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