Whisk together all ingredients for the cajun seasoning. Melt 2 tablespoons butter in a large skillet over medium heat. Stir in 1 teaspoon garlic, half of the cajun seasoning, and the rice, letting it toast for about a minute.
Stir in chicken broth, bring to a boil, then reduce to a simmer and cover. Cook for 15 minutes, stirring once or twice.
While rice cooks, toss shrimp with remaining 2 tablespoons melted butter, remaining garlic, and remaining cajun seasoning.
Stir shrimp into rice, cover, and cook 3-5 minutes longer until shrimp are pink and opaque.
Drizzle with the reserved 1 tablespoon melted butter, garnish with chopped parsley, and serve immediately.