Slice the eggplants lengthwise into ½-inch thick slices, then use the cookie cutter to cut out two rounds from each of the slices.

Place the eggplant rounds in a colander and toss them with 1½ teaspoons salt. Let them drain in the colander over a bowl in the sink for 45 minutes to remove excess moisture.

Bread the eggplant rounds in batches by coating them in the flour, then the eggs and then the breadcrumbs.

Heat a large skillet over medium heat and add enough oil to liberally coat the bottom of the pan. Pan-fry the breaded eggplant rounds in batches for 2 to 3 minutes, flipping them once until both sides are golden brown. Remove the cooked eggplant rounds and immediately transfer them to a paper towel-lined plate. Continue the pan-frying process, changing the oil as necessary, until all of the rounds are cooked.

Halve the brioche slider rolls and add 1 tablespoon of tomato sauce to the bottoms of the rolls. Stack an eggplant round atop the sauce, top it with another tablespoon of sauce and a piece of sliced mozzarella. Repeat the assembling process with all of the buns, transferring them to a cookie sheet lined with parchment paper.

Turn your broiler to high and carefully slide the cookie sheet under the broiler just long enough until the cheese melts. Immediately cap off the sliders with the tops of the buns and serve.

Chop up the discarded eggplant from the cutouts and roast it for a simple side dish, or use it to make Pasta Arrabiata with Roasted Eggplant.