As you shell the shrimp, I like to put the shells in a baggie, and stick it in the freezer, until I have a good amount saved up. Then, I have the makings of a lovely shrimp stock! But, that's a post for another day! If you're not interested in making a shrimp stock, you can still use the zip top bag to seal the shrimp-y smell out of your trash.
Once the garlic and shrimp are in the bowl, zest the lime over the shrimp, pour in 1 TBS of olive oil, add the salt and paprika, and stir it all together.
If you're not quite ready to cook these up, you can set this bowl, covered, in the fridge, for up to a couple of hours. When you're ready to cook juice two limes, and pour it over the shrimp, for up to twenty minutes, but you don't want to go any longer, or else your shrimp will get tough.
Place a nonstick pan over medium high heat, let it get super hot. These shrimp aren't going to take long to cook, but you want these to get a good sear on them, very quickly. While the pan is heating up, lay out a layer of paper towels on your counter, and lay your shrimp out on top of them. You need your shrimp to be dry, or else they will just steam in the pan, not sear. It would still be tasty, but it's not what I was after! Take another couple of paper towels, and pat the tops of the shrimp dry.
Once the pan is heated, and your shrimp are very dry, put them in the pan, with no olive oil, or butter, or any kind of fat. Turning the shrimp over once, cook these for 30-45 seconds, then turn the heat off and get them out of the pan. They will continue to cook with the carryover heat.
That is literally all there is to it! The lime in this really nice and bright, the garlic is just perfect and the paprika is a nice addition. The shrimp stay tender and juicy, and this will certainly be a constant in our shrimp recipe rotation!