Trim the cardoon ribs, pulling away any tough strings with a vegetable peeler, then cut into 8 cm / 3-inch batons. Drop the pieces straight into a bowl of water mixed with the lemon juice as you work to stop browning.

Bring a 24 cm / 9.5-inch stockpot of water to a boil with the 2 tbsp flour, 1 tsp salt, and the lemon water from the soaking bowl. Add the cardoons and simmer for 20 to 25 minutes until a knife slides in with no resistance but the pieces still hold their shape.

Drain the cardoons and spread them on a clean kitchen towel. Pat dry and let sit for 10 minutes until completely cool and dry to the touch, this step keeps the batter from sliding off in the oil.

Whisk the 150 g flour, eggs, sparkling water, 1/2 tsp salt, and pepper together in a mixing bowl until smooth and about the thickness of heavy cream. Fold in the parmesan if using.

Pour the oil into a 24 cm / 9.5-inch Dutch oven to a depth of 5 cm / 2 inches and heat to 175C / 350F on an instant-read or candy thermometer.

Dip 6 to 8 cardoon pieces at a time into the batter, letting the excess drip off, then lower them into the hot oil. Fry in batches so the pieces have room to puff and the oil temperature doesn't drop.

Fry for 3 to 4 minutes per batch, turning once, until the crust is deep golden and crisp. Lift out with a slotted spoon and drain on a wire rack.

Season each batch with flaky salt the moment it comes out of the oil. Let the oil return to 175C / 350F between batches before frying the next one.

Serve the cardi fritti hot with lemon wedges on the side.