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Set a medium skillet over medium-high heat. Add 1 teaspoon olive oil to the pan and tilt it to coat the bottom. Add the leafy greens to one half of the pan and put the bread in the remaining half. Use tongs to turn the greens in the pan until they begin to wilt. If you are using very delicate greens, such as baby spinach, this will happen in 30 seconds or so. Sturdier greens such as kale will take a few minutes.
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Once the greens are slightly wilted, flip the bread to the second side. Move the greens over to one side of the pan, leaving enough room to fry the egg. Add the remaining 1/2 teaspoon of oil into the empty space and crack the egg. Cook the egg to your liking: sunny side up, over easy, or over hard. For sunny side up, I set a lid on top of the pan (or invert a second skillet over it) to expedite the cooking process.
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Once the egg is cooked, lay the greens on the toast, top with the egg, finish with a pinch of salt and crack of black pepper. Serve