Heat pan over medium-high heat, add two tablespoons butter, and allow to melt and begin to foam. Add shallots and thyme. Season with salt and pepper. Stir to combine. Lower heat to medium and cook without stirring for 3-4 minutes. Stir and continue to cook until a dark golden brown. Remove from the heat.

Heat a griddle or skillet over medium heat. Butter each slice of bread on one side. Place two slices of bread on the pan, butter side down. Put half of the caramelized shallots on the bread. Top with half of the shredded cheese. Place the second slice of bread (butter side up) on top. Cover loosely and cook until the bread is golden brown. Flip and cook the other side. Serve and enjoy.