Peel, trim, and cut carrot into 1/4" dice. Halve and peel onion. Cut halves into 1/4" dice. Cut roasted red pepper into 1/4" dice. Stem and mince parsley. Pat shrimp dry, and season both sides with a pinch of salt and pepper.

Heat a medium pot over medium-high heat. Add 1 tsp. olive oil and shrimp to hot pot. Cook undisturbed until lightly charred on one side, 2-3 minutes. Flip shrimp, and cook until they reach a minimum internal temperature of 145 degrees, 30-60 seconds. Remove from pot. Reserve pot; no need to wipe clean.

Return pot used to cook shrimp to medium-high heat. Add 1 tsp. olive oil, carrots, half the onion and half the corn (reserve remaining of both for relish), and a pinch of salt and pepper. Cook, stirring occasionally, until vegetables soften, 4-5 minutes. Stir in sherry, shrimp base, tomato paste, and 4 cups cold water. Bring to a simmer, reduce heat to medium, and cook, stirring occasionally, 15-18 minutes. While soup simmers, make relish.

Heat a small non-stick pan over medium-high heat. Add 1/2 tsp. olive oil, roasted red peppers, remaining corn, and remaining onion to hot pan. Cook undisturbed until lightly charred, 2 minutes. Cook, stirring occasionally, until vegetables soften, 2-3 minutes. Remove from burner. Season with 1/4 tsp salt, a pinch of pepper, and a pinch of parsley (reserve remaining for garnish).

Carefully pour soup in 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 cream. Place over medium-high heat. Bring to a simmer and cook, stirring occasionally, until slightly thickened, 3-5 minutes. Season to taste with salt.

Pour soup in a bowl. Top with shrimp and relish and garnish with remaining parsley.