Using a grapefruit spoon or fingers, scoop out a 1-inch wide trough along the cut sides of the baguettes. Place 2 half-slices of the provolone cheese on each bottom half of the baguettes. Spoon 1/3 cup of the caponata on top of the cheese. Place the top halves on the baguettes and grill the panini until the cheese melts, about 5 minutes.
In a large skillet, heat the olive oil over medium-high heat. Add the onion and cook until translucent, about 3 minutes. Add the celery and eggplant and cook until soft, about 3 to 4 minutes. Add the red bell pepper and cook until crisp-tender, about 5 minutes. Add the tomatoes, raisins, and oregano to the pan. Simmer over medium-low heat, stirring frequently, until the mixture thickens, about 20 minutes. Stir in the vinegar, sugar, capers, 1/2 teaspoon of salt and 1/2 teaspoon of black pepper. Season, to taste, with more salt and pepper, if needed.