Reduce heat to medium. Add shallots, chile, and oregano, and sauté until shallots are sizzling, about 30 seconds. Add potatoes and garlic, cover, and cook, shaking pan often, until edges of potatoes begin to brown, about 5 minutes. Uncover, add wine, and cook, stirring occasionally, until liquid is nearly evaporated, 5 to 6 minutes.
Step 4
Add tomatoes, cover, and cook until tomatoes start to split and release their juices and potatoes are tender, about 8 minutes. Add shrimp, and cook, turning occasionally, until shrimp are cooked through and tomatoes are soft, 2 to 3 minutes. Season with salt and white pepper; stir in basil. Divide among 4 shallow bowls, drizzle with remaining 2 tablespoons oil, and serve.
