How to Make It
Heat oil in a large saucepan over low. Add onion, celery, garlic, and 1 teaspoon salt. Sauté until onions are translucent, 10 to 12 minutes. Add 2 cups milk; bring to a simmer, and cook until vegetables are tender, about 10 minutes. Remove from heat; let cool slightly.
While vegetables are cooking, prepare a large bowl of ice water and bring a large pot of water to a boil over high. Add peas to pot, return to a boil, and cook until peas are bright green and just tender, about 2 minutes. Remove peas with a slotted spoon, and immediately plunge into ice water. Return water in pot to a boil, add watercress, and cook until bright green and wilted, about 1 minute. Plunge watercress into ice water. Drain peas and watercress; set aside peas. Squeeze watercress to remove as much water as possible.
Combine peas, watercress, and remaining 1 cup milk in a blender. Process on high until smooth. Working in batches if necessary, add onion mixture to blender; process on high until smooth. Pour through a fine wire-mesh strainer into a bowl; discard solids. Season with remaining 1 teaspoon salt and white pepper. Cover and chill until ready to serve, at least 2 hours or up to 1 day.
Whisk together crème fraîche, 1 tablespoon chives, 1 tablespoon dill, tarragon, lemon zest, and 2 tablespoons lemon juice in a medium bowl. Gently fold in crab. Chill until ready to serve, at least 30 minutes or up to 2 hours.
Stir remaining 1 tablespoon lemon juice into soup. To serve, pour 3/4 cup soup into each bowl, add one large dollop of crab salad in center of soup, and drizzle with oil. Garnish with chives, pea tendrils, and black pepper, if desired.