Halve and peel onion. Slice ¼ the onion into thin strips and cut remaining into ¼" dice. Peel and cut potatoes into ¼" dice. Peel, trim, and cut carrot into ¼" dice. Shuck corn, rinse, and carefully remove kernels from cob. Stem and mince parsley. Pat shrimp dry.
Cook the Onions
Line a plate with a paper towel. In a mixing bowl, toss to coat sliced onions and cornstarch. Heat a large pot over medium heat. Add 3 Tbsp. olive oil and onions to hot pot and stir often until crispy, 4-6 minutes. Season with a pinch of salt. Remove to towel-lined plate. Reserve pot; no need to wipe clean.
Cook the Shrimp
Return pot used to cook onions to medium heat. Add 1 tsp. olive oil and shrimp to hot pot. Cook undisturbed until lightly browned, 1-2 minutes per side. Shrimp will finish cooking in a later step. Transfer shrimp to a plate. Reserve pot; no need to wipe clean.
Start the Soup
Return pot to medium heat. Add potatoes, diced onions, carrots, and a pinch of salt and pepper to hot pot, and stir occasionally until slightly tender, 5 minutes. Increase heat to medium-high heat, and add 2 cups water, wine, and corn to pot. Bring to a boil and cook until potatoes and carrots are tender, 8-10 minutes.
Finish the Soup
Stir in cream. Carefully pour half the soup in a blender. Remove clear insert from lid and cover blender with dish towel. It is very important to remove insert before blending to avoid exploding soup! Blend until very smooth, 1-2 minutes. Return blended soup to pot with remaining soup. Return to a boil and stir in shrimp and any accumulated juices and parsley until shrimp reaches minimum internal temperature of 145 degrees, 2-3 minutes. Season with salt to taste.