Lay out the 2 slices of bread. Using the full 2 tablespoons of room-temperature butter, spread an even layer on one side of each slice so both slices have a buttered side.

Turn the bread so the unbuttered sides are facing up. Slice the 3 ounces of cheddar into slices about 1/8–1/4 inch thick and arrange a single layer of cheese over the unbuttered side of one bread slice, covering the bread; overlap slices if needed.

Place the second slice of bread on top of the cheese with the buttered side facing out to form the sandwich.

Preheat either an electric griddle to about 275°F or a roomy sauté pan over medium-low heat.

Put the sandwich on the preheated surface, buttered side down. Cook undisturbed for 4–6 minutes, until the bottom is golden brown. Lower the heat if the bread is browning too quickly.

Carefully flip the sandwich with a spatula and cook the other side for another 4–6 minutes, until that side is golden and the cheese begins to melt.

If the bread is not yet the desired golden brown or the cheese isn’t fully melted, increase the heat to medium and continue turning the sandwich every 30–60 seconds, watching closely, until the bread is evenly toasted a deep golden brown and the cheese is fully melted.

Remove the sandwich from the heat, carefully cut in half if you like, and serve immediately.