On a griddle or in a large skillet, add olive oil over medium heat. Slice your feta cheese 1/4-inch thick and place slices in the oil. Let them sit for 3-4 minutes and they will develop a crispy crust. Flip and grill on the other side.
Meanwhile, toast your bagel and smear with a little mayo.
Crack your egg and scramble well. Add fresh olive oil to the griddle or skillet (about 1 teaspoon). Pour in your egg and let it setup for 1 minute. Use a good spatula to shape the egg into a square or round shape. Flip and cook for another 30-60 seconds.
Build your breakfast sandwich by adding the crispy feta slices to the bagel, top with egg, and baby spinach. Season with a pinch of salt and pepper. Add the top half of the bagel and wrap tightly in parchment paper or foil. Cut in half for easier eating.