Wash and dry all produce. Preheat oven to 450 degrees. Trim and halve Brussels sprouts lengthwise, then slice into shreds. Halve, peel, and dice onion. Mince garlic. Halve potatoes (quarter any larger ones so all potatoes are of equal size).

Toss potatoes on a baking sheet with a drizzle of olive oil and a large pinch of salt and pepper. Make sure all are cut-side down. Roast until golden brown and crispy, 18-20 minutes, tossing once halfway through.

Start the hash: Heat 1 Tablespoon butter in a large pan over medium heat. Add onions and toss until just softened, 2-3 minutes. Add red cabbage and garlic, and toss until tender, 3-4 minutes.
Add the Brussels sprouts: Add Brussels sprouts, and toss until veggies are tender and beginning to turn golden brown, another 4-5 minutes. Season to taste with salt and pepper. Remove pan from heat.
Heat a large drizzle of olive oil in another large pan over medium-high heat. Once hot, crack eggs and fry until edges begin to turn golden. Reduce heat to medium, and cover until whites are set but yolks are still runny, about 1 minute. TIP: Add a few teaspoons water to speed up cooking.

Toss potatoes into Brussels sprout mixture. Season to taste with salt and pepper. Divide hash between two plates, and top with fried eggs. Sprinkle with salt and a pinch of cayenne pepper (to taste). Enjoy!

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