Heat a skillet over medium high heat, add a splash of water and kale, and cook until wilted. Transfer to a plate.
Return skillet to the stove, drizzle with a little olive oil or butter. Crack egg over skillet and cook until edges have started to crisp, 1 - 2 minutes. Flip and cook until desired consistency (for an over-easy egg, this is 30 seconds to 1 minute more).
Assemble sandwich: top toast with avocado, then kale, then top with egg.