Bring a large pot of salted water to a boil. Add the spaghetti and cook as the label directs for al dente. Reserve 1 cup cooking water, then drain.
Meanwhile, season the shrimp with salt and pepper. Heat a large skillet over medium-high heat. Add 2 tablespoons olive oil, then add the shrimp in a single layer. Cook, turning halfway through, until the shrimp are curled and just cooked through, 2 to 3 minutes. Remove the shrimp to a bowl.
Reduce the heat to medium and add the remaining 2 tablespoons olive oil, the garlic and Fresno pepper to the skillet; cook, stirring, until the garlic is golden, about 1 minute. Add the oregano and cook until softened. Add the tomatoes and 1 cup water and bring to a simmer. Cook until the tomatoes burst and the sauce is reduced by half, about 10 minutes.
Add the shrimp, pasta and 1/2 cup cooking water to the sauce. Cook, tossing, until the shrimp are hot and the pasta is coated, 1 to 2 minutes, adding more cooking water as needed to loosen. Season with salt and pepper and stir in the basil.
Divide the pasta and shrimp among bowls. Sprinkle with more oregano and drizzle with olive oil.