Cook the shrimp: Fill a large bowl with water and add plenty of ice; set aside. Fill a large pot halfway with water. Add 1/4 cup dill, 2 smashed garlic cloves, a nice pinch of salt and a few grinds of pepper. Bring to a boil, then reduce the heat to medium low and simmer until fragrant, about 5 minutes. Add the shrimp; remove the pot from the heat and let sit, stirring occasionally, until the shrimp is pink and opaque, 2 to 3 minutes. Drain and transfer to the ice bath to cool.
Combine the remaining 1 cup dill, 1 grated garlic clove, the mayonnaise, sour cream, yogurt, cucumber, onion, lemon zest and sugar in a large bowl. Taste, then season with a pinch of salt and a few grinds of pepper.
Remove the shrimp from the ice bath, dry gently with a paper towel and coarsely chop. Stir into the dressing until combined.
Cut the iceberg lettuce into 4 wedges. Tear the first few layers from the center of each wedge to create a "bowl" in the wedge; divide among plates. Fill the lettuce bowls with the shrimp salad, letting it spill over the wedge. Garnish with chopped dill. Serve cold or at room temperature.