Heat the olive oil in a medium pot. Add the fennel and onion and cook over medium high heat until the vegetables start to brown, approximately 10 minutes. Add the sugar, salt and pepper and continue to cook, stirring constantly, until the mixture achieves a deep caramel hue, which should take an additional 2 minutes. Add the white wine and cook for 5 minutes, until most of the liquid in the pot has evaporated. Add the cannellini beans, Meyer lemon juice and vegetable broth, bring the mixture to a boil and reduce to a slow simmer.
Whisk together the sugar, white wine and nerigoma and set aside. Brush the cut side of each eggplant with the vegetable oil until all of the oil has been absorbed by the eggplant. Heat a skillet over medium heat and place the eggplant cut side down. Cook about 3-4 minutes until the eggplant starts to brown. Flip the eggplant over and cook an additional 3-4 minutes or until done (you can test for doneness by squeezing the sides of the eggplant gently with tongs or your fingers, it should feel soft). While the eggplant is cooking spoon the wine and nerigoma mixture over the cut side of the eggplant. Once done, flip the eggplant over and cook for 30 seconds to one minute, to caramelize the glaze.
To Serve: Divide the soup among three bowls. Top with the eggplant and 1 tsp. fresh fennel seeds.