Step 1In a food processor, blend the egg, garlic and lemon zest until light and frothy, about 30 seconds. Slowly add half of the grapeseed oil until it starts to emulsify and thicken. Add the tarragon and vinegar, and season with one-half teaspoon salt and a pinch of pepper. Pulse to combine.
Step 2While the machine is still running, drizzle in the remaining grapeseed and olive oils, then add the Parmigiano-Reggiano, blending until well combined. Adjust the seasoning. Keep in the refrigerator until ready to serve.
Step 1Place the aioli in a large mixing bowl. Thin the aioli out by stirring in the olive oil and sherry vinegar. Add the Parmigiano-Reggiano, shallots, lemon zest and chopped herbs, mixing to combine.
Step 2Pull the tender hearts of romaine apart and gently wash and dry the leaves. Toss the lettuce in the bowl of dressing gently with your hands and lightly but evenly coat each of the leaves. Cover the bowl with plastic wrap and refrigerate until final assembly, no more than 30 minutes before serving.
Step 1Heat the oven to 350 degrees. Place the 12 baguette slices on a baking sheet and brush with 2 tablespoons of the olive oil. Toast until golden, about 10 minutes.
Step 2Break the skin from the top of the burrata and spoon one heaping tablespoon of the soft cheese onto each of the crostini. Top each slice with a pinch of shallots, chives and fleur de sel and pepper to taste. Drizzle the remaining olive oil over the crostini.
Step 3Distribute the chilled salad evenly onto 6 chilled plates. Place two crostini onto each plate. Serve immediately.