Cut 2-inch holes out of the center of each bread slice, reserving the cut-outs.
Heat olive oil in a skillet over medium heat.
Dip bread into the whisked eggs, covering completely on both sides. Place each piece of dipped bread, 1 at a time, into the hot skillet; immediately crack an egg into the hole of the bread. Cook until egg is over-easy, about 1 minute per side.
Dip the bread cut-outs into the remaining whisked eggs and cook in the hot skillet until browned, about 2 minutes per side. Place the centers back into the center of each piece of bread to complete the top of the "basket".