Start by heating the vegetable oil in a large skillet over medium-high heat until shimmering and hot, which should give off a gentle crackling sound.
Add the shrimp to the skillet in a single layer, and cook for about 2–3 minutes until they begin to turn pink and develop a slight char around the edges.
Flip the shrimp and cook for another 2 minutes until fully pink and opaque. Remove the shrimp from the skillet and set aside.
Reduce the heat to medium, then add the minced garlic to the same skillet, stirring constantly for about 30 seconds until fragrant and just beginning to brown.
Stir in the Cajun spice blend, allowing it to toast slightly and release its aromas, about 30 seconds.
Pour in the chicken broth and hot sauce, scraping up any browned bits from the bottom of the pan to deglaze. Bring to a gentle boil and let it simmer for about 2–3 minutes until the sauce thickens slightly and turns darker.
Return the cooked shrimp to the skillet, tossing to coat them evenly in the spicy sauce. Cook for another minute until the shrimp are heated through and well glazed.
Remove from heat and squeeze in fresh lime juice over the shrimp. Give everything a quick toss to brighten up the flavors.
Transfer the shrimp to a serving dish and spoon over the smoky, spicy sauce. Serve hot, garnished with chopped herbs if desired.
