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Trim roots from the ramps and reserve. Finely mince ramps.
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Run the reserved root section of the ramps over each side of the stale bread. Cut each slice into 2 large triangles. Heat 2 tablespoons olive oil in a large skillet over medium heat. Press the bread into the hot oil. Sprinkle each slice with sea salt, pepper, and a pinch of minced ramps. Cook each side of the bread for 3 - 4 minutes, or until the croutons are a rich golden brown. Remove from heat and set aside.
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In a medium-sized bowl, whisk to combine 1 tablespoon of the white section of minced ramps, minced anchovies, lemon juice, Dijon, and a generous pinch each sea salt and pepper. Whisking vigorously, add 2 egg yolks. Next, adding just a drizzle at a time, whisk in the olive oil; mixture will thicken and become pale as you go. Taste mixture, and add more sea salt as needed.
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Spoon 4 - 6 tablespoons of dressing over the spinach, tossing very gently. Add the Parmesan, toss, and then layer more sea salt and pepper to taste.
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Fill a wide saucepan with cold water and bring to a boil. Poke the narrow side of each egg with a pin to make a small hole. When water comes to a boil, add the apple cider vinegar and a generous amount of sea salt. Turn heat down so the water bubbles gently. Using a slotted spoon, lower the eggs still in the shell into the water, cook for 10 seconds, and remove. Working quickly, crack the eggs one at a time into a shallow dish and lower into the water. Cook eggs for an additional 4 minutes.
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Meanwhile, plate the spinach salad and add a crouton to each plate. Use a slotted spoon to remove poached eggs from the water. Set each egg on a crouton; finish with grated Parm, minced ramps, sea salt, and pepper. Serve immediately.