Cut off the tops of the jalapenos and scoop out the seeds. Pat the shrimp dry and generously season with salt. Insert 1 shrimp into each jalapeno, leaving the tail sticking out.
Whisk 3/4 cup flour, the cornstarch, Old Bay and beer in a medium bowl until smooth; set aside. Heat 2 inches of vegetable oil in a large pot or Dutch oven over medium heat until a deep-fry thermometer registers 350 degrees F. Whisk the remaining 3/4 cup flour and 1/2 teaspoon salt in a shallow bowl.
Working in batches, dredge the jalapenos in the flour, shaking off any excess, then dip in the beer batter, coating the shrimp and jalapeno completely. Fry, stirring occasionally, until the shrimp are cooked through and the jalapenos are golden and crisp, about 5 minutes. Remove with a slotted spoon and drain on paper towels; season with salt. Serve with malt vinegar.