Mix 2 TBSP mayo and 1 TBSP whole grain mustard together in a small bowl.
Heat a nonstick skillet over low-medium heat. Spread a small amount of plain mayo on one side of a slice of bread and place it mayo side down in the skillet.
Spread a quarter of the mayo/mustard mixture on the surface of the bread. Top it with shredded gruyere, then half the shredded chicken and the fresh thyme. Follow the chicken with a slice of havarti torn into pieces, then the prosciutto. Finally, sprinkle a little more of the grated gruyere and half a slice of havarti torn into pieces.Work quickly, making sure you’re creating even layers that go all the way to the edges of the bread while leaving room for the cheese to melt through all the crevices and hold the bread together.
To close the sandwich, spread a quarter of the mayo/mustard mixture on a second slice of bread and place it face down on top of the assembled sandwich in the pan, and then spread a dollop of plain mayo on the top surface of the bread, all the way to the edges.
Use a spatula to press down on top of the sandwich as the cheese melts. Lift the bottom of the sandwich up periodically just enough to check that it’s browning, not burning, and adjust the heat if necessary.
When the cheese has melted and the bottom piece of bread is toasty and golden brown, use a spatula to flip the sandwich over and continue cooking for another 3-4 minutes until the bread is toasted and the cheese has melted enough to hold the sandwich together.
Repeat to make the second sandwich. Enjoy!