Step 1

In a large skillet over -medium-high heat, melt 1 tablespoon of the ghee. Add the bread slices and cook without flipping until golden on one side, 1–2 minutes. Transfer to a plate toasted-side down and set aside.

Step 2

In the same skillet, melt the remaining 2 tablespoons of ghee. Add the mushroom, season with salt and black pepper, and cook, pressing the mushroom down with a spatula and flipping once, until golden brown and crisp on both sides, about 4 minutes total. Move the mushroom to one side of the skillet and top it with the cheddar. Crack the egg into the open space and cook until the white is set, about 2 minutes. Flip the egg and turn off the heat.

Step 3

Spread mustard on the untoasted sides of the bread. Top one slice with the lettuce and pickled onions and the other with the mushroom, then the egg. Close the sandwich, cut it in half, and serve.