The smoky eggplant complements the spicy harissa and salty feta, all contrasted with the pillowy-soft challah, yielding a sandwich that’s a medley of interesting flavors and textures. I used wholegrain pretzel challah from a popular Los Angeles bakery, but any type of challah will do.
Slice the eggplant into 8 to 10 quarter-inch slices. Place in a colander and sprinkle generously with salt. Allow to sit for 10 to 20 minutes.
Rinse the eggplant and pat each slice dry.
Heat a large, deep skillet over a medium-high flame. Pour in 1 inch of oil and heat to 350°F (or until water added to the oil sizzles). Add the eggplant slices and fry until golden (2 to 3 minutes on each side). Remove from heat and allow the oil to come to room temperature.
Meanwhile, to assemble each sandwich, smear harissa on one slice of challah, top with feta and fried eggplant, and cover together with a second slice of challah.
Pour the oil out of the skillet, return it to the stove, and heat over a medium flame. Place 1 or 2 sandwiches in the pan (depending on space), and fry each sandwich on both sides until deeply brown, adding butter to the skillet as needed. Serve immediately.