Sprinkle each side of the sliced eggplant with salt. Let sit for 5-10 minutes on a towel {or paper towel}. Wipe off any moisture that accumulates.
Preheat a grill pan/panini press. Add eggplant and grill for about 3 minutes per side. Remove from grill and set aside to cool for a few minutes.
Spread goat cheese on each slice of grilled eggplant. Top half of the slices with salmon and a few slices of red bell pepper. Top with a slice of eggplant {with the cheese side facing the inside}.
Grill the eggplant until the cheese is melted, about 3-5 minutes. Enjoy!