Cook the bacon, stirring occasionally, in a medium Dutch oven over medium heat, until crisp, about 5 minutes. Add the oil and onion and cook, stirring, until soft, about 3 minutes. Add the tomato paste and stir until it loses its vibrant red color, about 30 seconds. Scatter the flour over the onions and cook, stirring to make a paste, about 1 minute.
Stir in the broth and half-and-half until well combined with no lumps of flour. Add the potatoes, 1 teaspoon salt and 1/2 teaspoon pepper. Bring to a boil, then reduce the heat to medium-low, and simmer covered until the potatoes are tender, about 15 minutes.
Add the shrimp and cook until just opaque, about 4 minutes. Adjust the seasoning with additional salt and pepper and the consistency of the soup with additional water if too thick. Ladle the soup into bowls, drizzle with oil and top with the basil and more pepper.
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