Start by bringing a pot of salted water to a boil for the eggs. Once boiling, carefully add the 6 eggs and cook for 6½ minutes for jammy yolks with set whites. While the eggs cook, cut the white bread into 1-inch cubes and slice the baby kale into thin ribbons. Measure out all dressing ingredients and set them near your food processor for easy access.

Heat 3 tablespoons of olive oil in a large skillet over medium-high heat. Once shimmering, add the bread cubes and toast for 4 to 5 minutes, stirring occasionally, until golden and crispy on all sides. Season immediately with ¼ teaspoon salt and ¼ teaspoon pepper. Transfer to a paper towel-lined plate to cool while you prepare the remaining components.

Add the 2 egg yolks, 2.5 teaspoons Dijon mustard, 2 teaspoons minced garlic, and 12 anchovy fillets (finely minced into a paste) to a food processor. Pulse until the anchovies are fully incorporated and the mixture is smooth. Add ½ cup lemon juice and pulse to combine. With the machine running, slowly drizzle in 1.75 cups olive oil in a thin stream—this gradual addition emulsifies the dressing and creates a creamy texture. Once thickened, pulse in ½ cup freshly grated Parmesan, 2 teaspoons salt, and ¾ teaspoon black pepper. Taste and adjust seasoning as needed.

Bring a large pot of salted water to a boil. Add the 8 cups of broccoli florets and cook for 4 minutes until bright green and tender-crisp. Drain the broccoli in a colander, then immediately transfer to a bowl of ice water to stop the cooking and set the color. Once cooled, drain thoroughly and add the sliced kale from Step 1 to a large mixing bowl.

Pour about three-quarters of the dressing from Step 3 over the broccoli and kale mixture, then add the cooled croutons from Step 2 and ¼ cup lemon juice. Toss gently but thoroughly until all components are evenly coated. Add ¼ cup Parmesan and toss again. I find that tossing just before serving keeps the croutons crispier, but you can assemble this salad up to an hour ahead if needed. Transfer to a serving platter or individual plates.

Remove the cooled eggs from Step 1, peel them gently under cool running water, and slice each into quarters. Arrange the egg quarters over the top of the salad. Drizzle with any remaining dressing and season with a pinch of fleur de sel and freshly cracked black pepper to taste. Serve immediately while the croutons are still crispy.