Place oven rack in top position and preheat to 400°F.
In a large oven-proof skillet, heat 5 teaspoons of the olive oil over medium heat. Add garlic and onion, and cook until fragrant and soft, 3-5 minutes.
Add wine and scrape up any brown bits from the pan. Increase heat to high and add tomatoes, Italian seasoning and salt and pepper to taste. Cook, stirring occasionally until softened, about 6 minutes.
Add orzo and chicken broth and bring to a simmer. Cover, transfer to oven, and bake until liquid is mostly absorbed, 10 to 12 minutes. Remove from oven and stir in Parmesan.
Toss shrimp with remaining 1 teaspoon of olive oil and season with salt and pepper. Place shrimp on top of orzo.
Heat broiler to high. Place skillet back in the oven and broil until shrimp are opaque throughout (about 4 minutes for jumbo size). Sprinkle with fresh basil and red pepper flakes and serve.