You can choose to leave the shrimp tails on or off. It does not change the taste at all. The tails are left on purely for presentation.
Cooking Shrimp:
Once the shrimp is clean, pat them dry with a paper towel and place into a mixing bowl.
Add pressed garlic cloves, lemon juice, salt, crushed red pepper flakes, parsley, and paprika. Mix well to make to all shrimp is coated evenly.
Preheat a cooking pan over medium to medium-high heat first.
Once the pan in hot, add oil and spread it around. Add shrimp in one even layer and let them cook until opaque on that side. This will only take a couple of minutes.
Add butter while shrimp is cooking.
Flip each shrimp onto the other side and let them cook until opaque on that side.
Take shrimp out of the pan right away so they don't keep cooking and garnish with a little more parsley if you'd like.
How long do shrimp take to cook:
On average, shrimp take 2-3 minutes to cook completely. Jumbo shrimp could take 4-6 minutes, depending on the actual size and thickness. You are looking for the shrimp to turn completely opaque to be done, and no more.
Optional Sauce:
Right after you take the shrimp out, melt a tablespoon of butter in the pan, then add 1/2 cup of white wine. Let it simmer and reduce by about half over medium heat.
Whisk in 1/2 tablespoon of lemon juice and a couple of tablespoons of vegetable or chicken stock. There will be a lot of flavor left in the pan from cooking the shrimp but you may still need a little bit of salt. Taste and add a pinch of salt if necessary.