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First, make the slaw. Shred the Brussels sprouts using a mandolin. Toss them together with the purple cabbage, lemon juice, apple cider vinegar, pepitas, salt, and pepper. Place in the fridge.
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Next, bring a pot of water to a rolling boil. Knock the heat back so the bubbles aren't so big. Place the raw egg in the water. Set a timer for five minutes. Prepare a bowl of ice and water. After five minutes, carefully remove the egg, and transfer to the ice water.
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Toast the bread. Smash the half of avocado on the toast. Season with salt and pepper. Top the bread with the slaw.
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Carefully crack and peel the eggshell. Place the egg over the toast and use the side of a fork to bust the yolk open.
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Enjoy immediately.
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Slaw can last a day or two in the fridge.