Pour some water into a saucepan and add in salt according to your taste. Set saucepan of salty water on stove and bring it to boil over medium heat. Now, add in haricots verts and cook them for 3 to 5 minutes or until crispy and tender. Remove from heat and drain the cooked haricots verts with the help of a large sieve. Rinse them under cold running water for few seconds until cool to handle. Set aside to cool well.
In the meantime, take a blender and add in the mayonnaise, yogurt, lemon juice, basil, chives and anchovies. Seal the blender by placing its lid at the top and blend ingredients until smooth.
Unseal the blender gently and season the yogurt dressing with salt and ground black pepper.
Pour half of the yogurt dressing into a medium bowl. Add in crabmeat and half of the avocado slices. Toss these ingredients until finely coated.
Place the boiled haricots verts in another large mixing bowl and add in the romaine, and croutons. Top with the remaining avocado slices the yogurt dressing. Stir the ingredients until slip in thoroughly.
Now, arrange the romaine salad on a large serving platter and top it with the halved cherry tomatoes. Spoon the crab mixture right in the center of the platter.
Serve at once.