Combine butter and miso paste together until they are completely blended.
Bring a pot of water to boil and add a pinch of salt. Gently add the eggs one at a time. Cook for 5 minutes (use a timer). Remove eggs from the water with a slotted spoon and run under cold water to cool slightly, about 1-2 minutes. Crack shell, set eggs aside.
Slice bread and spread a tiny bit of olive oil. Broil it in the oven until one of the sides turn golden brown.
Take the four slices of bread and brush the butter onto one side of each piece. Top with egg on top.