1. Spread bread slices on a large cutting board. Spread 1 tsp butter on one side of each slice. Place slices, buttered side down, back on board. Divide chipotle mayonnaise among slices, 1 tsp on each.
2. Divide shredded cheddar among 6 of the slices, 1/4 cup on each, compacting slightly so that cheese sticks together. Top each with sliced tomato and 1/4 cup of the shredded Gouda, compacting slightly. Sandwich with remaining bread slices, mayo side down.
3. Heat a large, lidded nonstick skillet over medium-low heat. Once heated, add 2 sandwiches to skillet. Cover and cook 2 to 3 minutes, compressing gently with spatula. Flip sandwiches and cook 2 to 3 more minutes.