Preheat a grill to medium high. Make the dressing: Puree the yogurt, mayonnaise, lemon juice, Worcestershire sauce, chives, basil, and salt and pepper to taste in a blender. Transfer to a small bowl, cover and refrigerate until ready to use.
Make the burgers: Form the beef into four 6-ounce patties, about 3/4 inch thick; press the center of each patty with your thumb to make a 1/2-inch-deep indentation. Season the patties on both sides with salt and pepper. Lightly brush the grill grates with vegetable oil, then grill the patties, indentation-side up, until marked on the bottom, about 5 minutes. Flip and cook until marked and slightly firm, about 3 more minutes for medium doneness. Remove the patties to a plate and let rest 5 minutes. Grill the buns, cut side down, until lightly toasted, about 1 minute.
Top the bun bottoms with the lettuce, tomatoes, burger patties, alfalfa sprouts and avocado. Drizzle with the dressing, then cover with the bun tops.