Preheat oven to 450 degrees. Lightly grease a large baking sheet.
Make sure your shrimps are thawed, peeled, and deveined. I prefer tail off for this recipe. Pat the shrimp very dry with paper towels and add to a bowl. Toss with the brown sugar, smoked paprika, chipotle chili powder, garlic powder, onion powder, pepper, and a big pinch of salt, until evenly coated.
Spread the shrimp onto the baking sheet. Bake 8-10 minutes, turning once halfway through baking time. If desired, broil on high for the final 1-2 minutes. Remove from the oven. If desired, brush with bbq sauce.
Meanwhile, bring a large pot of salted water to a boil. Cook the pasta according to package directions. Drain and rinse under cool water to stop the cooking process. Set aside.
In a food processor, combine the mayonnaise, yogurt, parmesan, garlic, lemon juice, dijon mustard, anchovy paste, and a pinch of salt and pepper. Blitz until very smooth and creamy. Taste and adjust seasonings as needed.
Dump the pasta into a large mixing bowl. Add the chopped romaine, tomatoes, cheddar cheese, and avocado. Toss with 1/3-1/2 cup of the Caesar dressing.
Divide salads amongst bowls or plates. Top with the shrimp. Serve alongside additional Caesar dressing, as desired.