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Preheat oven to 400 degrees F. Oil a 12-cup muffin tin and set aside.
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Toss shredded potatoes with 1 teaspoon sea salt. Let sit 2 minutes. Then, working in batches, place potatoes in a flour cloth (or other lightweight cotton kitchen towel) and wring out the water. Wring out all the water you can.
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Toss wrung shredded potatoes with the olive oil and spices. Divide potato mixture between the 12 cups and press down firmly. Bake until tops are golden and crisp, 50 - 60 minutes.
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Make toppings 20 minutes before you're ready to serve the meal. First, set a skillet over medium/medium-low heat. Add 2 tablespoons olive oil. When oil's hot and shimmering, add garlic and sauté until quite fragrant, about 4 minutes (edge heat down so garlic doesn't brown). Add kale and a pinch sea salt, and continue cooking until kale's cooked down completely, 7 - 10 minutes. Taste, and add more sea salt as needed.
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To make mornay, melt butter in a large saucepan over medium heat. Whisk in flour and a pinch sea salt, and then gradually whisk in milk, allowing mixture to thicken up between additions. Once all the milk has been added, turn heat to medium-low and cook 10 minutes, stirring frequently. Remove from heat, add cheese, and stir until smooth. Add black pepper or sea salt to taste.
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To poach eggs, bring a wide, deep-sided pan filled with water to a gentle boil.
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When water boils, add sea salt and apple cider vinegar. Gently lower eggs (still in the shell) into the water, cook 10 seconds, and remove with a slotted spoon. Crack eggs one a time into a small, shallow bowl, tip each into gently boiling water and cook 4 minutes – this cook time will yield set egg whites and runny yolks.
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To plate, run a knife along the sides of the muffin tin and use a spoon to gently lift the hash browns out. Set 2 - 3 on each plate. Top with sautéed kale, 1 - 2 poached eggs, and mornay. Serve immediately.