Carefully slice the avocado evenly in half and remove pit.
Heat a cast iron pan until hot, swirl in olive oil, and place avocado, meat side down in pan. Turn to low and let sit while you toast butter.
In a small pan, heat butter over medium heat, swirling to prevent it from burning. Once butter begins just to turn brown, swirl in fennel, mustard, and cumin seeds. Let them sputter for 30 seconds, pull pan off and splash in vinegar.
Place avocado on small plate flesh side up. Pour brown butter into each pit cavity evenly and devour with a spoon!