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Heat up a pan with 1 teaspoon of olive oil on medium high heat. Add in the Brussel sprouts and cook for 3-4 minutes until the leaves get dark brown and caramelized. They should have a nice sweet taste, but not too bitter. Set aside.
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Whisk together the oil, vinegar and dill, set aside.
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For the poached egg, heat up a small pot of water to a simmer but not full boil. Add in a pinch of salt and carefully crack an egg into the pot. Don't let the water boil too much or it will break up the egg white. Use a slotted spoon to carefully scrape the egg off of the bottom of the pot. Cook time for a soft poached egg should be no more than 3-4 minutes.
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Take the egg out of the water and let sit on a piece of clean paper towel to drain off excess water.
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Mix together all of the salad ingredients with some of the dressing and put on a plate. Put the Brussel sprouts beside the salad, drizzle the rest of the dressing on them and top with the poached egg.
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Break the yolk and mix in with the salad to add a nice creamy texture to the dressing.