Place thawed shrimp in a medium bowl and rinse well with cold water. See notes if you need to remove any veins. To remove the tails from each shrimp, hold the shrimp with one hand, and with the other hand, pinch the tail and pull it off. Discard tails. Give shrimp a good rinse again to remove any stray pieces of shell.
Melt butter in a large skillet (extra-large is best.) While butter is melting, press or mince garlic. When the butter is melted, add the garlic to the pan and cook for about 30 seconds, being careful not to burn it.
Add drained shrimp to the pan and spread it out in a single layer, if possible. Cook for 2 ½ minutes on the first side, then start to flip each shrimp over. Cook for another 2 ½ minutes on the second side, or until shrimp is no longer translucent. The cooked shrimp will be white, with reddish-orange accents
When the shrimp is cooked, add lime juice from half a lime, cilantro and paprika or Old Bay seasoning. Taste to see if you need to add salt. (It will depend on the shrimp you bought. Also, Old Bay contains salt.)
Serve the shrimp with the remaining lime half for anyone who wants extra lime juice. Store leftovers in the refrigerator for up to three days.
Best shrimp to useI recommend buying large, frozen, raw, peeled, deveined shrimp with tails on. (If you buy two pounds of peeled shrimp without tails, you'll get more shrimp than what I used in the recipe and and will need to increase the butter and seasonings a bit.)Look for shrimp that are deveined nicely.A shrimp "vein," or thick black line along its back, is actually the digestive tract. I've learned the hard way that some brands of shrimp sold as "deveined" still contain several veins. If that's the case with the ones you bought, you'll need to remove them before cooking. A shrimp tool(affiliate link) is helpful for that job. Note that the recipe prep time does not include deveining the shrimp.Can you use a substitute for cilantro?If you don't like fresh cilantro, dried cilantro is much milder. You also could substitute parsley, or even skip the herbs.