Slather the bread with the butter. You will butter only one side of each slice, using 1 tablespoon per slice.
Heat a heavy-bottomed skillet that has a lid over medium-low heat.
Add one slice of bread to the pan, butter side down. Top with cheese. Add the second slice of bread, butter side up.
Toast for 4 to 6 minutes, until golden brown, with the lid on. Then carefully, using a spatula, flip the sandwich. I like to use a few fingers on the top of the sandwich as I flip. Return the lid and toast for 4 to 6 more minutes.
Notes
Mild cheddar cheese melts better than sharp cheddar cheese, which can turn out oily and clumpy. Mild cheddar melts very smoothly.