Make the caponataPlace eggplant pieces in a mixing bowl and add pinch of salt; rub salt evenly into the pieces. Let rest until eggplant starts to release some water into the base of the bowl.Fill a heavy-bottomed pot with a few inches of olive oil and place over medium heat. Carefully add eggplant pieces to oil in batches, frying until pieces are golden brown around the edges. Reserve eggplant and discard all but 1 to 2 tablespoons oil.Add eggplant, onion, garlic, and thyme to pot and place over medium-low heat. Cook for 25 to 30 minutes, stirring regularly, until eggplant is softened.Add pepperoncini, brown sugar, cocoa powder, and salt and pepper to taste. Add a splash of balsamic vinegar and stir to combine. Continue to cook over medium-low heat until liquid is reduced, about 10 minutes more. Adjust seasonings as needed. Remove from heat and stir in chopped basil.Make the polentaIn a saucepan, combine milk, heavy cream, bay leaf, and a pinch of salt and place over medium-high heat until simmering. Slowly whisk in polenta, then lower heat and stir often until polenta is soft and creamy, about 30 to 45 minutes. Remove bay leaf and add butter, salt, and pepper to taste.To serve, place polenta in a serving dish and top with the caponata. Garnish with Parmigiano Reggiano and basil leaves.