Bring water to a boil in a medium saucepan over high heat. Add 2 teaspoons salt. Whisking constantly, add cornmeal in a slow, steady stream, switching to a wooden spoon when cornmeal becomes too thick to whisk. Reduce heat to medium, and cook, stirring often, until thick and creamy, about 15 minutes. Stir in butter, cover, and keep warm over low heat.
Preheat oven to 350 degrees. Lightly butter a 2-quart baking dish. Heat oil in a large skillet over medium-high heat, then add onion, garlic, bell pepper, chile, and a pinch of salt. Cook, stirring often, until onion is light gold and vegetables are tender, 10 to 12 minutes. Add turkey, and cook, breaking up large pieces with a wooden spoon, until cooked through, 5 to 7 minutes. Stir in tomatoes and juices, stock, cumin, oregano, and cayenne. Reduce heat to medium, and cook, stirring, until most of the liquid has evaporated and mixture resembles chili, about 10 minutes. Stir in olives, and season with salt and pepper.
Spread 1 1/2 cups cornmeal into bottom of prepared dish with a wet spatula. Spread turkey mixture on top, then spread remaining 2 1/2 cups cornmeal on top. Sprinkle with Monterey Jack. Bake until golden brown and cheese is melted, 35 to 40 minutes. Let stand for 15 minutes. Serve with avocado, tomatoes, cilantro, red onion, and lettuce.