Preheat oven to 350°. Lay bread on a baking sheet and drizzle with about 2 tbsp. oil. Bake until toasted and light golden brown, about 5 minutes. Set aside.
Heat 2 tbsp. oil in a large nonstick frying pan over medium-high heat. Cook eggplant, stirring often, until softened and starting to brown, about 8 minutes. Transfer to a bowl and set aside.
In the same pan, cook garlic in remaining 2 tbsp. oil, stirring, until fragrant, about 1 minute. Add celery, bell pepper, and olives, stirring to combine, and cook until softened, 5 to 8 minutes. Stir in 1/4 cup water, the vinegar, tomato paste, raisins, and pine nuts and cook until heated through. Stir in reserved eggplant, salt, and sugar, then mix in herbs.
Serve caponata with ricotta on the toasted bread.
Make ahead: Chill caponata up to 2 days and store toasts airtight up to 2 days.
Note: Nutritional analysis is per serving.