Preheat oven to 400°F and line a baking sheet with foil. Prick the eggplant all over with a knife, and roast for about an hour, turning halfway through, until soft and smooshy.

When cool enough to touch, scoop out insides into a colander set in the sink, and let drain for 30 minutes.

Meanwhile, peel, dice, and boil the potatoes until easily pierced with a fork. Drain and put potatoes into a large bowl and mash.

Once the eggplant is drained, add it to the potatoes. Stir in egg, goat cheese, salt, pepper, and enough breadcrumbs so that the mixture holds shape, but is still sticky.

Put remaining breadcrumbs into a shallow bowl or plate. Form eggplant mixture into patties and roll in breadcrumbs, then transfer to a lined baking sheet.

Chill patties in the refrigerator for at least 20 minutes. (If you're freezing any, do so after the 20 minute fridge visit.)

Heat oil in large frying pan over medium. Fry croquettes in small batches, making sure not to crowd the pan, for about 3 minutes total.

Transfer to paper towels to drain and serve with aoili, vinaigrette, or just a squeeze of lemon juice.