How to Make It
In a small saucepan, combine the carrot juice and shallot and boil over moderate heat until reduced to 2 tablespoons, about 6 minutes. Transfer to a blender. Add the vinegar and let cool slightly, then puree until smooth. With the machine on, slowly blend in 2 tablespoons of the olive oil. Season the vinaigrette with salt and pepper.
In a medium bowl, whisk the lemon juice with the remaining 1/4 cup of olive oil. Add the onion, crab and sorrel and toss gently. Add the avocado, season with salt and pepper and gently fold together. Mound the salad on plates, drizzle the carrot vinaigrette around it and serve.