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1
Chop off the leafy top of the eggplant, peel it if you don't like the skin, and cut it into 3/4- to 1-inch cubes. Add these to a colander set in the sink, sprinkle with the 1 1/4 teaspoons salt, and toss with your hands. Let the eggplant hang out for 30 to 45 minutes, so the eggplant can sweat out its excess water.
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2
In the meantime, heat the oven to 400u00b0F, and line a sheet pan with a silicone mat or parchment.
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3
After the eggplant is done being salted, dry it as much as possible with towels, then dump the cubes onto the sheet pan. Drizzle with the melted butter and toss with your hands until the eggplant is completely coated.
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4
Roast the eggplant for 15 to 25 minutes, tossing halfway through, until it's as tender as you like. I like to lean toward al dente here, to mimic lobster chunks, but softer-smushier eggplant is delicious, too.
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5
Once the eggplant is out of the oven, let it cool for a bit while you work on the dressing. Take a spoonful of the diced celery and set it aside (we'll use it in a bit). Now combine the rest of the celery, the mayo, lemon juice, black pepper, and celery in a medium bowl. Stir, then add the eggplant, and stir again. Taste and adjust the lemon juice, salt, and black pepper as needed.
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6
Heat a cast-iron skillet over medium heat. Spread the outside of the buns with butter and sprinkle with salt. When the pan is hot, add the buns, one flat side facing down. Cook them for 1 to 2 minutes per side, until golden-brown and toasty, making sure to get the bottoms, too.
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7
Transfer the warm buns to a plate and evenly distribute the eggplant salad inside each. Sprinkle the tops with the reserved diced celery and eat right away.
