Step 1

Position a rack in the middle of the oven and preheat to 325 degrees.

Step 2

In a large cast-iron skillet over medium heat, heat the oil until it shimmers. Add the onion and salt and cook, stirring often, until the onions turn translucent, 4 to 6 minutes.

Step 3

Add a splash of water and then, working in batches, enough greens to fill the pan. Cook, stirring often, until the greens are wilted down enough to add more. Keep adding the greens and cooking them down until they are all wilted, adding another splash of water to help steam the greens as they cook down. Cook until most of the moisture has evaporated and the greens are tender, 6 to 8 minutes. Taste, and season with more salt as needed.

Step 4

Lay the bread slices on a rimmed baking sheet and divide the sliced cheeses evenly among them. Bake for 5 to 6 minutes, or until the cheese is just melty.

Step 5

Remove from the oven and divide the greens among two of the bread slices, covering the cheese. Cover with the other two bread slices, cheese side down, and press the sandwiches together. Spread the mayo on the outside of both the top and bottom of each sandwich (to help form a crust when they’re pan-fried).

Step 6

Wipe the skillet out to remove any greens residue and return it to medium heat. Add 1 tablespoon of the butter, swirling it to melt and coat the pan, and place the sandwiches in the skillet. Set another skillet (or similar flat, heavy object) on top of them to weigh them down for even cooking. Cook until they are nicely browned on the bottom, then flip and repeat, adding the remaining 1 tablespoon of butter and weighing them down again. Cook until the second side is nicely browned. Cut each sandwich in half and serve hot.