Heat oil in a large Dutch oven over medium-high heat. Add shrimp to pan; sauté 2 minutes or until shells turn bright orange. Add onion, carrot, and celery; sauté 3 minutes or until tender. Add tomato paste, stirring well with a wooden spoon. Cook 8 minutes or until tomato paste turns orange, stirring constantly. Add 5 cups water; bring to a boil. Remove from heat.
Place half of shrimp mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Pour into a large bowl. Repeat procedure with remaining shrimp mixture. Return to pan. Bring to a simmer over medium heat; remove from heat. Let stand for 10 minutes. Strain the shrimp mixture through a fine sieve over a bowl. Discard solids.