Sprinkle the eggplant slices with salt and let them sit for about 30 minutes to draw out moisture. Rinse and pat dry with paper towels.
Set up a breading station: Place flour in one shallow dish, beaten eggs in another, and breadcrumbs in a third.
Dredge each eggplant slice in flour, dip in the beaten eggs, and coat with breadcrumbs.
Heat olive oil in a large skillet over medium heat. Fry the breaded eggplant slices for about 3-4 minutes on each side until golden brown. Drain on paper towels.
In a small bowl, mix the goat cheese with chopped tarragon, salt, and pepper.
Spread the goat cheese mixture on the bottom half of each ciabatta roll. Layer with fried eggplant slices and a generous spoonful of marinara sauce. Top with arugula and the other half of the roll.
Serve immediately, or you can grill the assembled sandwiches on a panini press for a warm, melty option.