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1
Chop the mizuna into bite-sized pieces, and chiffonade or chop the basil. (You should end up with about 5 cups of greens, total.) Toss to combine, and set aside.
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2
In a large skillet, heat 1 tbsp olive oil over medium-high heat. Add mushrooms and cook, stirring occasionally, for about 10 minutes, or until golden and crisp all over. Remove from the pan with a slotted spoon and transfer to a paper towel-lined plate to drain.
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3
While the mushrooms cook, bring a large saucepan of water to a bare simmer.
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4
Reduce the heat under the skillet to medium and add the remaining 3 tbsp oil. Add shallot and saute for 1 minute, or until translucent. Add vinegar, mustard, salt, and pepper, and heat just until the vinegar bubbles. Turn the heat to low and keep the dressing warm.
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5
While the vinaigrette cooks, add a large pinch of salt to the simmering water, then gently crack in the eggs. Poach for 3-4 minutes, or until the whites are set but the yolks are still runny.
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6
Divide the greens between two serving plates. Distribute the mushrooms evenly between the two plates, then pour over the vinaigrette from the pan. Remove the eggs from the water with a slotted spoon, carefully draining off as much water as possible, and transfer 1 egg to each plate. Season the tops of the eggs with pepper. Serve immediately, with hunks of crusty bread for mopping up the dressing.
