Prepare the onions, carrots, burdock and mitsuba and add them to a large bowl, breaking up any clumps onions. Make sure your vegetables are very dry (use paper towels to dry them if they aren't).

Prepare a wire rack lined with several sheets of paper towels. Heat a heavy bottomed pot with 1-inch of vegetable oil to 360 degrees F (180 C).

Toss the vegetables together with the flour until the flour is evenly distributed.

Add the cold club soda to the vegetables and then mix to combine. It's okay if there are a few small lumps of flour but there should not be any water at the bottom of the bowl. Be careful not to overmix the batter.

The easiest way to shape the batter and ensure it does not fall apart while frying is to shape it on a spatula first, and then lower the whole spatula into the oil, using a second spatula to scrape the fritter off the first one.

Fry the Kakiagé until they are no long limp and then flip and fry the other side (about 1-2 minutes)

Fry the second side until it crisps as well (an additional 1-to 1 ½ minutes).

When the Kakiagé is crisp (but not yet browned), remove from the oil, draining as much oil from them as you can over the pot before transferring to your prepared rack.

Serve the Kakiagé on a sheet of paper with a side of good finishing salt.