You can make the dressing and cauliflower ahead of time.
Bring a large pot of salted water to a boil.
Clean and slice 2 small or 1 medium leek. Heat 5 T. olive oil in a small skillet and saute the leeks until they begin to brown and crisp, then turn off the heat.
Trim 2 small or 1 medium head of Cauliflower and separate the florets. Cut the larger florets in halves or thirds so that they are approximately the same size as the small ones.
Drop the florets into the water. When the water returns to a boil, turn off the water and let the cauliflower sit for 3 minutes. The florets should be tender but still crisp. Drain and rinse with cold water, then allow to dry.
When the leeks are cool, transfer them and the oil into a small bowl. Whisk in 3 T. fresh lemon juice, a pinch of thyme, and salt and pepper to taste. Allow the dressing to sit for 10 minutes.
Toss the cauliflower with 2/3 of the dressing. Let it sit for half an hour, then toss again and leave it another half hour.
Poach 8 eggs.
Wash and spin dry 1 small head romaine lettuce. Roughly chop the leaves, then toss with the remainder of the dressing.
Make a bed of romaine on each plate, then a bed of cauliflower on top of it. Place the eggs on the cauliflower.