Assemble each sandwich by layering 1/4 cup Gruyere cheese and 1/2 cup of Monterrey Jack on one slice of bread. Sprinkle with a little fresh thyme, about 1/4 teaspoon per sandwich. Top with another slice of bread and gently press down on the sandwich with the palm of your hand.
Heat a buttered skillet or griddle over medium-low heat.
Place grilled cheese onto skillet or griddle and cook until lightly toasted, about 3 minutes per side.