Heat the oil in a large wide pot or medium Dutch oven over medium heat. Add the bacon and cook, stirring occasionally until crisp, about 5 minutes. Add the onion and cook, stirring, until soft, about 3 minutes. Add the tomato paste and stir until toasted, about 30 seconds. Scatter the flour over the onion and cook, stirring with a wooden spoon to make a paste, about 1 minute.
Pour in the broth and milk, stirring until the mixture is smooth. Add the potatoes and season with salt and a generous grinding of pepper. Bring to a boil, then reduce the heat to medium-low, and simmer, covered, until the potatoes are tender, about 15 minutes.
Stir the shrimp into the soup and cook until just opaque and firm, 4 to 5 minutes. Remove from the heat and stir in the basil. Adjust the consistency of the soup with a little water if it?s become too thick and adjust the seasoning with additional salt and pepper.
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