Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs for al dente; drain and return to the pot.
Meanwhile, core, halve and seed the tomatoes. Blend the tomatoes, 1/4 cup olive oil, the garlic, oregano, 3/4 teaspoon salt and a few grinds of pepper in a food processor to make a chunky sauce. Add to the pasta and toss to combine.
Heat a large skillet over medium-high heat. Season the shrimp with salt and pepper. Add the remaining 1 tablespoon olive oil to the skillet, then add the shrimp in a single layer; cook, turning once, until just cooked through, 2 to 3 minutes. Add the shrimp to the pasta, tossing to combine.
Divide the pasta and shrimp among bowls. Drizzle with olive oil.