Pat the shrimp dry. Dry shrimp sear better. Place them on a paper towel and blot both sides.
Toss with 1 tablespoon olive oil.
Mix the blackening spice. In a small bowl, combine smoked paprika, garlic powder, onion powder, thyme or oregano, cayenne, brown sugar, salt, and black pepper. Sprinkle over the shrimp and toss to coat evenly.
Start the orzo base. In a medium saucepan, heat 1 tablespoon butter and 1 tablespoon olive oil over medium. Add the minced garlic and cook 30 seconds until fragrant.
Toast the orzo. Stir in the orzo and toast for 1 to 2 minutes, stirring often.
It should smell nutty but not brown deeply.
Add broth and simmer. Pour in the broth, bring to a gentle simmer, and reduce heat to medium-low. Cook uncovered, stirring occasionally, for 8 to 10 minutes until the orzo is al dente and most liquid is absorbed. If it looks dry before the pasta is done, add a splash more broth or water.
Make it creamy. Stir in the remaining 2 tablespoons butter, the Parmesan, and milk or half-and-half if using.
Season with salt and pepper to taste. Lower the heat to keep warm; the orzo should be creamy and loose, similar to risotto. Add a spoonful of liquid if it tightens too much.
Blacken the shrimp. Heat a large skillet (cast iron is ideal) over medium-high until hot.
Add a thin film of oil if the pan is dry. Arrange shrimp in a single layer and cook 1.5 to 2 minutes per side, just until opaque with a dark, crusty edge. Do this in batches if needed to avoid steaming.
Finish with lemon. Zest half the lemon into the orzo and squeeze in a little juice.
Taste and adjust salt, pepper, and acid. You want a bright finish to balance the richness.
Serve. Spoon creamy orzo into bowls, top with shrimp, and sprinkle with chopped parsley. Add extra Parmesan and lemon wedges on the side.