Brown butter in a large skillet or dutch oven over medium high heat. Then add the chopped yellow onion. Cook until translucent, roughly 5 minutes then add the minced garlic. Cook for another 3 minutes, stirring often.
Add the dry orzo to the pan and toast it by stirring it around in the butter, onions, and garlic for 1 minute. Then add in the chicken broth.
Stir in the chopped rosemary, paprika, black pepper, and red pepper flakes. Let the orzo cook through until the chicken broth is mostly gone
When the orzo is 90% cooked through, add the milk and shredded parmesan cheese. Stir to combine. Add the juice of ¼ lemon.
Add the shrimp to the dish and stir so that the shrimp are cooked through. You want the shrimp to be pink all the way through.
Add extra rosemary or salt if desired. Serve and enjoy!