In a large cast iron skillet, heat olive oil until shimmering. Add garlic and sautè for about 30 seconds. Add dry wine, Worcestershire sauce, broth, lemon juice and hot sauce to the pan and bring to a boil for about 3 to 5 minutes, allowing the mixture to become thick and saucy.
Add the shrimp to the pan. Turn them over after 2 minutes and then cook for about 1 more minute, or until the gray shrimp begin to turn pink. Lower heat to a very low simmer.
From a height add the pepper, salt, paprika, and thyme over the top of the shrimp. It may seem like a lot of pepper, but this is the secret ingredient that makes this dish scrumptious.
Add the butter over the shrimp by tablespoons. Then turn the shrimp over and continue to add butter over it. The butter will emulsify, adding a sheen to the sauce. Once the butter is incorporated, remove the pan from the heat.
Serve the shrimp and sauce over cheesy grits, rice, or on its own in a bowl with plenty of bread to sop up the shrimpy sauce.