Step 1

Heat 1 Tbsp. extra-virgin olive oil in a large nonstick skillet over medium-high until shimmering. While oil heats up, trim green parts of 12 scallions so they fit in skillet. Add scallions to skillet (hairy bits still attached; we’ll discard them later on) and toss to coat in oil. Season with salt and pepper and cook, undisturbed, until deeply charred, about 4 minutes. Toss and continue to cook, tossing occasionally, until softened and charred all over, 2–3 minutes longer. Transfer scallions to a cutting board and let cool; reserve skillet.

Step 2

Trim and discard hairy ends of scallions, then chop crosswise into ½" pieces. Transfer to a small bowl. Finely chop ⅓ cup pickled jalapeños. Transfer to bowl with scallions and toss to combine.

Step 3

Arrange 4 ½"-thick slices country-style bread on cutting board. Spread 1 Tbsp. mayonnaise on one side of each slice.

Step 4

Using a vegetable peeler, shave 4 oz. cheddar cheese into long ribbons.

Step 5

Place 2 bread slices (mayonnaise side down) in skillet. Arrange shaved cheddar over, overlapping as necessary so they in the confines of the bread. Top cheese with scallion-jalapeño relish.

Step 6

Arrange 2 slices of American cheese over relish. Close sandwiches with remaining 2 slices of bread (mayonnaise side up).

Step 7

Heat skillet over medium and cook sandwiches, undisturbed, until deeply golden brown and crisp underneath, 5–7 minutes. (We start the sandwiches in an unheated skillet so they can gently and evenly brown, and don’t end up burning. This is how you get that perfect exterior crunch.) Using a spatula, carefully turn sandwiches. If anything goes awry, just push your sandwich back together and continue. Season cooked side with salt and reduce heat to medium-low and continue to cook until evenly golden brown and cheese is melted, 4–5 minutes longer. This time, we’re cooking them at a lower heat because the skillet is already hot from the previous side, the opposite process of the previous step. Transfer both sandwiches to a cutting board. Season other side of sandwich with salt.

Step 8

Mix ¼ cup whole-grain mustard and 2 Tbsp. Dijon mustard (if using) in a small bowl.

Step 9

Cut grilled cheese sandwiches in half. Serve with mustard alongside for dipping.