Pour 2-3 inches of vegetable oil into a heavy-bottomed pot, making sure it's deep enough to submerge the calamari rings. Attach a deep-fry thermometer to the pot, if you have one, and heat the oil to 350°F over medium to medium-high heat.
In a shallow dish, mix together the flour, cornflour, salt, black pepper, garlic powder, paprika, dill, and cayenne pepper.
Pour the buttermilk into another shallow dish.
Working with a few pieces at a time, dredge the calamari rings in the flour mixture, shaking off any excess. Dip them into the buttermilk, letting excess drip back into the dish, then return them to the flour mixture and coat again. Transfer the coated rings to a tray while you finish the batch.
Carefully add a handful of calamari rings to the hot oil, being sure not to overcrowd the pot so the temperature stays close to 350°F. Fry, turning occasionally, until the coating is crisp and light golden brown and the calamari feels just firm, 2-3 minutes. The rings should sizzle steadily and float to the surface as they finish.
Use a slotted spoon or tongs to transfer the calamari to a paper towel–lined plate or a wire rack set over a baking sheet to drain. Immediately sprinkle with a little extra salt, if desired. Repeat with the remaining calamari, allowing the oil to come back to temperature between batches.
Serve warm.