Melt the last tablespoon of butter in a pan on low heat. Add the onions and let them cook slowly, about 20 minutes. As the onions darken, stir them occasionally, adding a bit of water to loosen up the sticky onion bits on the bottom and keep them from burning. Leave the onions until they’re dark purple. They will now be sweet and caramelized.

Melt 1/2 tablespoon of butter in a small pan on medium heat. Place the two slices of bread in the pan and let them cook for about 2 minutes, then lift them with a spatula to check whether they’re golden brown underneath. When they are, flip ’em over. Add the rest of the butter to the pan to make sure the second side of the toast becomes just as golden as the first. Sprinkle the top of the bread with salt and pepper. Once the second side is golden, set the bread on a plate to await its topping.

Spread them over toast and top with slices of sharp cheddar, salt, and pepper. Put the toast back in the pan and cover with a lid until the cheese is bubbly, then serve it up.