Make the garlic bean spread. Combine the garlic cloves with thyme, rosemary, and ½ cup olive oil in a medium saucepot. Heat the oil over low heat and continue to gently simmer for 10 minutes or until the garlic cloves are lightly browned. Remove from heat and let sit for 10 minutes.
Remove and discard the herbs. Blend the garlic cloves with ¼ cup of the oil, cannellini beans, 1 teaspoon dijon, and 1 tablespoon lemon juice until smooth. Season with salt and pepper. Set aside.
Heat 2 tablespoon oil in a saute pan over medium-heat heat. Add the diced eggplant and cook until caramelized on all sides, about 7-8 minutes.
Add the shallots and black garlic and saute until the shallots are tender, about 3 minutes. Add the canned tomatoes, 1 ½ tablespoon pomegranate molasses, and 1 teaspoon sugar and bring to a boil. Reduce heat to low and simmer for 20 minutes, stirring frequently. Season the eggplant with salt and pepper.
Toast the bread and smear the garlic bean spread on top. Spoon a generous amount of the braised eggplant on the toast and finish with chopped mint and a sprinkle of sea salt. Serve immediately.