Greek shrimp with spinach, feta, and orzo

7 tablespoons extravirgin olive oil, divided;

12 ounces uncooked orzo pasta;

4 cups lightly packed baby spinach or stemmed and shredded chard;

11⁄2 cups crumbled feta cheese, divided;

1⁄2 cup grated Parmesan cheese;

2 pounds extra-large (21 to 25 count) shrimp, peeled and deveined (thawed if frozen);

4 garlic cloves, peeled and chopped;

1 (28-ounce) can crushed tomatoes;

1⁄4 cup dry white wine;

2 teaspoons dried Mediterranean oregano;

1⁄2 teaspoon crushed red pepper flakes;

1⁄2 cup chopped flatleaf parsley;

1 teaspoon kosher salt;

1⁄2 teaspoon ground black pepper.

Preheat the oven to 400°F. Brush a glass or ceramic 9 × 13-inch baking dish with 1 tablespoon of the oil.
Cook the orzo according to package directions. Drain well in a colander and return to the same pot. Stir in 3 tablespoons of the oil, the spinach, 1⁄2 cup of the feta cheese, and the Parmesan. Spread the orzo mixture in the bottom of the prepared baking dish and cover with foil to keep warm.
Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the shrimp and cook only until they start to turn opaque, about 1 minute. The shrimp will finish cooking in the oven. Arrange the shrimp over the orzo.
Heat the remaining 2 tablespoons of oil in the skillet. Add the garlic and cook until you can smell the aroma, about 30 seconds. Stir in the tomatoes, wine, oregano, and red pepper flakes. Simmer uncovered, stirring occasionally, until the mixture reduces to the consistency of pasta sauce, about 5 minutes. Stir in the parsley. Season with the salt and pepper. Spoon the sauce over the shrimp and orzo.
Bake until the shrimp are opaque, about 10 minutes. Sprinkle with the remaining 1 cup of feta cheese and serve hot.