Devein, clean, and pat dry shrimp. Then mix with Cajun rub and set aside.
Heat a large skillet on high heat. Add in oil. When oil is hot and shimmery, sear shrimp in 3 batches, making sure to keep space in between the shrimp. Sear shrimp until both sides are just golden brown and the inside is just cooked through. Remove from pan and set aside. Repeat for the next 2 batches, adding in extra oil to the pan before each batch.
After shrimp is removed from the pan, add oil. Keep heat on medium. Then add aromatic vegetables: garlic, onion, and green onion. Sauté and sweat until the vegetables have just softened, about 5 minutes. Then add in butter and flour. Cook on medium heat until flour is slightly brown and nutty.
Then add cream and chicken broth to the pan. Mix well into the flour mixture. Then add in Worcestershire sauce and soy sauce. Allow to cook on medium for 2-3 minutes until the sauce reduces and becomes thick. Add in shrimp and cook together for just 1 minute. Check for seasoning and add salt, pepper, and/or red pepper flake as needed.
Take shrimp off of heat and serve on top of grits.