1. Fill pot with oil 1 1/2 inches deep.
2. Heat oil over medium-high to 375°F. Prepare a baking sheet lined with paper towels and a wire rack for finished onion rings to drain. While oil is heating, trim ends from onions, peel, and cut crosswise into 1/2 inch thick rings. Gently separate rings, discarding innermost rings and broken pieces.
3. In a large bowl, whisk flour, cornstarch, baking powder, and pimenton. In a small bowl, whisk together beer, mustard, and honey.
4. Add wet ingredients to dry, stirring well to combine. Dip onion rings into batter a few at time, turning to coat thoroughly. Shake off excess batter and carefully lower into hot oil. Cook until dark golden brown on each side, 2-4 minutes, turning halfway through.
5. Remove with a wire strainer to prepared wire rack, sprinkle lightly with salt while hot.
6. Continue to fry onion rings, pausing in between batches to allow oil to return to 375°F.
7. Serve immediately. Allow oil to cool completely before straining and storing.