Soak squid rings in a bowl of buttermilk for one hour.
Prepare the remoulade.
Start with remoulade. In a large bowl, mix the celeriac, apple, mayonnaise, mustard, pickles, and lemon juice together thoroughly, with a generous sprinkling of salt and some freshly ground black pepper, so it all becomes one sauce. It will keep in the refrigerator for up to two days.
Heat oil in a saucepan or deep-fryer to 350F (180C).
Add flour and corn starch to a bowl. Season with salt and pepper and stir together. Pour some of dry mixture into a plastic bag. Add squid rings that have soaked in buttermilk. Pour in rest of dredge and shake up bag. Strain dredged squid through a sieve to remove excess. Place the squid in the hot oil, and fry in small batches, turning if necessary, for even cooking. When evenly browned, remove to paper towel to drain.
Toss fried calamari in a bowl with chopped pea shoots, red chillies, and a dash of salt. Plate with lemon wedges and serve with remoulade.