In a small bowl, mix the mayonnaise and Dijon mustard together until smooth. Spread the softened butter evenly on the outer face of each bread slice (these will contact the pan). On the inner face of one slice, spread the mayo-mustard mixture evenly.

Assemble sandwich

Place one slice of Swiss cheese on the mayo-mustard–coated bread. Layer the three slices of deli ham evenly on top of the cheese. Add the cornichons or pickle slices on top of the ham, distributing them evenly. Place the second slice of Swiss cheese over the ham and then top with the remaining bread slice, buttered side facing out.

Grill

Heat a nonstick skillet or griddle over medium to medium-low heat. Add 1 tsp unsalted butter and let it melt and coat the pan. Carefully place the assembled sandwich in the skillet. Cook for 3–4 minutes until the bottom is golden brown and the cheese begins to melt. Press gently with a spatula or a second pan to ensure even contact.

Flip and finish

Flip the sandwich and cook the other side for another 2–3 minutes, lowering the heat if the bread browns too quickly. Continue until cheese is fully melted and both sides are golden and crisp. Total grilling time should be about 5–7 minutes.

Rest and serve

Remove the sandwich from the skillet and let rest on a cutting board for 1 minute to set. Slice in half on the diagonal if desired. Season with freshly ground black pepper to taste and serve immediately.

Optional add-ins

If using caramelized onions, prepare them in advance by cooking thinly sliced onion in 1 tsp butter over low heat for 20–25 minutes until deep golden; drain excess moisture before adding to the sandwich during assembly.

If using greens, add them inside the sandwich after grilling (or briefly on the warm cheese) so they retain a bit of texture and don't wilt excessively.