Use olive oil to lightly coat a 9-inch square baking pan. Wash the millet, then combine the millet and amaranth or teff with the stock in a small saucepan with a tight-fitting lid. Bring to a boil, then reduce the heat to a simmer and cook, covered, for 30 minutes. Lift the lid and stir it a few times during cooking. After 30 minutes, it should be a thick, porridgey consistency. Keep cooking and stirring until it begins to form a more solid mass, about 5 minutes. Stir in the Parmesan, salt, and pepper. Scrape into the baking pan and smooth the top. Chill in the refrigerator for at least 3 hours.
Unmold the polenta onto a cutting board and slice into triangles or bars. Reserve.
In a large sauté pan, heat 2 tablespoons of the olive oil and sauté the shallots and carrot over medium heat. When they are tender, add the anchovy paste, olivada paste, lemon zest, and canned tomatoes. Bring to a boil and cook for a few minutes, until thick. Add the tuna, stir it in, and add lemon juice to taste. Keep warm.
Preheat the oven to 450°F. When hot, place a heavy baking pan in the oven to heat for 5 minutes. Take it out, drizzle 1 tablespoon of the olive oil on the pan, and put the polenta slices in the oil. Drizzle the remaining tablespoon of oil over the top of the polenta, and place in the oven. Bake for 5 minutes, then turn the slices over with a spatula. Bake for 5 minutes more, until the edges of the slices are crispy.
Serve the polenta on plates, topped with the tuna sauce and basil.