Bring water to a boil in a large pot over high heat. Add salt, sugar, and dill sprigs; stir until sugar has dissolved. Pour in shrimp and cook until the shells turn pink, and the meat is no longer translucent, 3 to 4 minutes. Strain the shrimp through a colander, discard dill sprigs, and chill until cold in the refrigerator, about 30 minutes.
Once shrimp have cooled, peel and devein them; discard the shells. Whisk together oil, vinegar, minced dill, salt, and pepper; toss with shrimp meat to coat. Cover, and chill overnight in the refrigerator; serve with sprigs of fresh dill.