Pour the beer into a medium-size bowl and stir in the vodka. Slowly whisk in the flour and the paprika. The batter should be fairly thick, but also easy to stir. Set aside in a warm place. "Press" the garlic clove into another bowl and stir in the olive oil and shrimp. Season lightly with salt and pepper. Set aside. Pour the oil into a heavy-bottomed pot (or, alternatively, a deep-fryer). Heat the oil slowly to 370 F. Use a candy thermometer to monitor the temperature. Line a baking sheet with a kitchen towel or paper towels to drain the shrimp once they are cooked.
Preheat the oven to 250 degrees F.
Arrange the basil leaves on a sheet pan. Put the pan in the oven for 2 minutes, just to wilt the basil a bit, if the basil is young and tender this step is not necessary. Wrap a basil leaf around the middle of each shrimp like a belt. When ready to serve, dip the shrimp into the batter and drop, in small batches, into the oil. Fry until crispy, turning on both sides with a slotted metal spoon. Add the lemons into the oil and fry until crispy. Drain them on the lined baking sheet and season immediately with salt. Transfer to a serving platter and serve immediately.
This is the simplest and best batter recipe. I use it at the restaurant all the time.