We melt the butter in a small prep bowl in the microwave. We unroll the defrosted phyllo dough and place one sheet on our wax paper covered counter. We cover up the dough that we are not working with so it does not dry out. Using our pastry brush, we brush quickly with the butter. We tear off a two inch width of the sheet. The rest we fit into one of the cups of the muffin tin – mostly worrying about covering up the sides. We fold the two-inch piece width in quarters and fit in the bottom of the same muffin cup. We repeat with the other five sheets of dough, fitting them into every other cup of the muffin tin.
We break each egg carefully into each phyllo-filled muffin cup and bake in the oven for 10-20 minutes depending on how runny or well-cooked we like the yolks. We remove the baked egg with a small offset spatula when it is the desired doneness.
We serve the baked eggs sprinkled with salt and pepper.