In a large skillet, melt the 1 tablespoon of unsalted butter over medium heat. Once melted, add the 1 cup of uncooked converted brown rice and toast it for about 2 minutes, stirring frequently to prevent burning.
Pour in the 2 cups of low sodium chicken broth and bring to a boil. Once boiling, reduce the heat to low, cover, and let it simmer for about 20 minutes or until the rice is tender and the liquid is absorbed.
While the rice is cooking, heat 2 teaspoons of olive oil in a separate pan over medium-high heat. Add the 1-1/4 pounds of peeled and deveined shrimp and sauté for approximately 3-4 minutes until they turn pink and opaque. Remove the shrimp from the pan and set aside.
In the same pan, add the remaining 2 teaspoons of olive oil and the 1/2 cup of frozen peas. Cook for 2-3 minutes until the peas are heated through.
Once the rice is done, fluff it with a fork, then add the sautéed shrimp and peas to the skillet. Stir to combine and season with salt and pepper to taste.
Sprinkle 2 tablespoons of grated Pecorino Romano cheese over the top and mix gently. Garnish with 1 tablespoon of chopped parsley before serving.