This is a nice little bite as an appetizer, and the sauce that is left is great for dipping bread... OR I thought it might be good if you made it with smaller shrimp and used the whole dish as a sauce for pasta.
The main flavoring for this dish is a compound butter.
Compound butter is a mixture of butter and other ingredients: onions, garlic, herbs, cheese, spices, citrus zest...
The butter can be used as a finishing sauce for a good piece of beef (as they do in many nice restaurants- it melts right over the warm meat) or various types of seafood. When melted, the butter can be used as a dip for breads or vegetables.
When making a compound butter, you can store it in the freezer or refrigerator wrapped in plastic or waxed paper and shaped into a log. Just slice of what you need!
If you want to serve individual portions with 2 shrimp per person, the shrimp can be baked in 10 individual ramekins, otherwise place all the shrimp and compound butter in an 8x8 or 9x9 baking dish. Baking time will be less than 20 minutes... I would say perhaps start with 10 and check the shrimp occasionally after that to make sure it's translucent and cooked.
To clean the shrimp, peel off the shell- but leave the last joint and tail of the shrimp intact. Make a shallow cut down the back of the shrimp, exposing the vein. Pull this out, discard, and rinse the shrimp in cool water.
Dill and Shallot Shrimp
20 jumbo shrimp/king prawns, uncooked, peeled and deveined
3/4 stick (6 T butter) at room temperature
2 T finely chopped dill
1 small shallot, finely minced
1/3 c white wine
Preheat oven to 375 degrees with the rack in the middle.
Season shrimp with a bit of salt and pepper and set aside.
Mix the dill and shallot into the softened butter along with 1/4 t each of salt and pepper. Place about a teaspoon of the butter in each ramekin and add two shrimp on top of the butter. Divide the white wine among the ramekins (about 1 1/2 t per ramekin) and divide the remaining butter among each of the dishes, on top of the shrimp. Place the ramekins on a sheet pan and put the pan in the oven. Bake for approximately 20 minutes, until the shrimp are just cooked through.