Preheat the oven to 375 degrees F. On a baking sheet, place the baguettes and toast in the oven. Set aside.
In a large saute pan, heat the olive oil over medium-high heat until almost smoking.
Add the garlic, onion, celery, thyme, eggplant and a couple of pinches of salt. Stir together, reduce the heat to medium, and cook until the eggplant turns golden (5-6 minutes). If it looks a little dry, add 1 tablespoon of oil.
Add the tomato paste, currants, pine nuts, cinnamon, cocoa powder and red pepper flakes and continue to cook for 3 minutes more. Add the vinegar, stir well and allow to evaporate (30 seconds-1 minute). Add the sugar, water, salt and pepper to taste and cook for 5 minutes more, then remove from the heat.
Stuff each baguette piece with about 1/2 cup of the caponata and top with Pecorino Romano and provolone. Place the stuffed bread on a baking sheet and place in the oven. Bake until the cheese is nicely melted. Remove and serve immediately.