Sprinkle the shredded cheddar cheese evenly over the tuna-topped muffin halves, or lay torn cheese slices over the top, covering as much of the surface as you can.
Cover the skillet with a lid (or a large baking sheet if you don’t have a lid) to trap the heat. Cook over medium-low heat for 5–8 minutes, or until the bottoms of the muffins are lightly crisped, the tuna mixture is hot, and the cheese is melted and gooey.
Carefully lift one muffin half with a spatula to check the bottom; it should be lightly golden and a bit crisp around the edges. When they look and smell toasty and the cheese is fully melted, remove the muffin halves to plates.
Let the tuna melts sit for a minute to cool slightly, then serve warm. They’re meant to be eaten with a fork and knife, but around here, plenty of folks just pick them up once they’re cool enough to handle.
For a slightly lighter version, use light mayonnaise or replace half the mayo with plain Greek yogurt; the mustard and relish will keep things tangy. If you enjoy more crunch, stir in extra finely chopped celery or a tablespoon of minced onion. Swap the cheddar for whatever cheese you have—American, Colby, or Swiss all melt beautifully and change the character just a bit. To stretch the recipe, add another English muffin and thin the tuna mixture with an extra spoonful of mayo. If you like a little heat, add a pinch of cayenne or a few dashes of hot sauce to the tuna mix. For a more browned top without using the oven, turn the heat to low once the cheese has melted, remove the lid, and let the muffins sit another minute or two so the cheese gets tiny golden spots. Leftover tuna mix keeps well in the refrigerator for a day or two; the next time, you can spread it over fresh muffin halves in the skillet and have another quick, comforting meal with almost no effort.