While the oil heats, pour the buttermilk into a small bowl. In a second small bowl, stir together the flour, paprika, chili powder, and black pepper. When the oil is ready, working in batches to avoid crowding, dip the shallot slices in the buttermilk, allowing the excess to drain back into the bowl, and then dredge them in the flour mixture, shaking off the excess. Slide the shallots into the hot oil and fry for 2 to 3 minutes, until golden brown and crisp. Using a slotted spoon, transfer to the prepared plate to drain. Repeat with the remaining shallots.