Directions

1. Preheat oven to 375 degrees. Place tortillas on a baking sheet. Brush both sides with 1 teaspoon oil; sprinkle with 1/2 teaspoon chili powder, and season with salt and pepper. Bake until golden brown and crisp, turning once, 8 to 10 minutes. Let cool, then break into pieces.
2. Heat broiler. In a large bowl, toss shrimp with remaining teaspoon each oil and chili powder. Season with salt and pepper. Lay shrimp flat on a broiler pan, and cook until browned and opaque throughout, turning once, 3 to 4 minutes.
3. In a small bowl, whisk together mayonnaise, lime juice, Parmesan, anchovies, and up to 2 tablespoons water. Season with salt and pepper.
4. To serve, toss lettuce with dressing. Divide among plates, and top each with shrimp and broken tortillas. Garnish with more Parmesan.