Start a large pot of salted water over high heat and bring to a boil. You will want to add the linguine just as you are beginning to cook the shrimp.
Peel the shrimp, leaving the tails on. To butterfly the shrimp, use a sharp paring knife and make an incision down the back of each shrimp about ¼-inch deep. Remove the vein and discard.
Rinse the peeled and butterflied shrimp in a colander and let drain.
In a shallow bowl or pie pan whisk together the flour, salt, paprika, pepper flakes, and black pepper.
For the milk I measure it into a 1-cup liquid measuring cup and use that for dipping the shrimp.
Heat 3 Tablespoons of the olive oil in a large saute pan over medium-high heat.
With the side of a wide knife crush the garlic cloves and add them to the oil. When the oil is hot and the garlic is fragrant, remove the crushed cloves from the pan.
Meanwhile, when the water is boiling, add the linguine and let it cook while you are cooking the shrimp. Just before the pasta is al dente, remove the pan from the heat. The linguine will continue to cook in the hot water until you are ready to transfer it to the sauce.
Dip shrimp into the milk then dredge in the flour mixture. Be sure the flour covers the whole shrimp, including in the butterflied crevice.
When the oil is hot, stand the shrimp up on their butterflied backs and cook until golden, about a minute or so. Turn the shrimp and cook each side until golden brown all around. Shrimp should be cooked and golden brown in 5 to 6 minutes. Remove to a nearby warm plate.
I do the shrimp in 2 batches, 10 shrimp each batch. After the first batch add 2 to 3 more Tablespoons olive oil to the pan.
When all the shrimp are cooked and out of the pan, pour the white wine into the pan scraping up the yummy browned bits. Bring to a boil and cook until reduced by about half.
Add the butter to the wine mixture. When the butter is melted add the lemon juice and remove from the heat.
Using a spaghetti server or tongs transfer the cooked pasta into the sauce. If necessary, add some of the pasta water until there is enough sauce to satisfy you.
Stir in the chopped parsley.
Stand the shrimp up on top of the pasta and garnish with lemon slices.