Preheat vegetable oil on the stove (or in a fryer, if you have one) to 350°F.
In a separate bowl, combine 1 cup of flour, cornstarch, and baking powder, and sieve. Add the beer and mix with a whisk until smooth.
In a small bowl, combine ½ cup flour and celery hearts and mix gently to coat. Dip each piece in the beer mixture and fry in vegetable oil until golden brown. With a slotted spoon, remove from oil and place on a paper towel; season with salt to taste. Serve immediately.