Make the tartar sauce. Whisk together all the ingredients, along with plenty of freshly cracked black pepper. Taste for seasoning and adjust.
Prepare the radicchio. Discard any dry or brown outer leaves. Gently peel leaves off so that you have 8 pieces large enough to hold a piece of fish (roughly 6 inches wide).
Make the batter. Whisk together the dry ingredients. Add the wet ingredients and whisk until just combined. It’s okay if there are a few lumps: you don’t want to overmix the batter.
Prepare your frying station. Add the oil to a large pot or dutch oven. The oil level should be about halfway up the side of the pot: significantly less will inhibit frying. Much higher and it gets dangerous. Heat the oil to 375°F. Line a sheet pan with a wire wrack or paper towels.
Fry the fish. Dip a piece of fish into the batter so that it’s evenly coated. Allow a bit of the batter to drain off and then carefully place the fish in the hot oil. To reduce splash when adding fish to the pot, don’t drop it. Rather, get as close to the oil as possible and lay the fish away from you. Repeat the process with a few more pieces of fish. Don’t overcrowd the pot. Make sure each fish can swim freely in the oil. You may need to fry in batches.
Plate. Place a piece of fried fish on each wrap and top generously with tartar sauce. Serve with lemon wedges and chili oil if you like.