Bring a large pot of salted water to a boil. Add the pasta and cook according to the package directions until al dente. Drain.
While the water comes to a boil, drizzle a little oil in a large cast-iron skillet and heat over medium heat. Add the shallots and cook, stirring occasionally, until they begin to soften, 3 to 4 minutes. Add the garlic and cook, stirring often, until golden brown and fragrant, 2 to 3 minutes. Do not let it burn.
Next, add the diced tomatoes with their juices, coconut milk, crushed red pepper and a sprinkle each of salt and black pepper. Stir and reduce the heat to a simmer. Let simmer until the flavors meld and the sauce thickens slightly, 5 to 7 minutes.
Add the shrimp, stir and cook until they turn pink and firm up, 3 to 5 minutes. Remove from the heat and stir in the spinach and chopped basil. The heat from the sauce will wilt the spinach. Taste for seasoning and add more salt and black pepper, if needed.
Divide the pasta among bowls. Ladle some of the sauce over each portion, garnish with basil leaves and serve right away.