Grate and salt the squash. Remove any developed seeds or spongy flesh, leaving tender skin on. Coarsely grate the squash and place in a colander. Toss with the salt and leave for 10 minutes.
While the squash rests, coarsely grate the halloumi, finely slice the spring onions and chop the herbs. Grate the lemon zest, beat the egg and measure out both flours.
Transfer the squash to a clean tea towel. Gather the edges and squeeze firmly over the sink, repeating until very little liquid comes out. The squash should be damp but compact.
Combine the squeezed squash, halloumi, spring onions, herbs, lemon zest and black pepper in a bowl. Stir in the beaten egg, then fold in the plain flour and cornflour until evenly combined. The mixture should hold together in a rough mound.
Add enough olive oil to coat the base of a wide frying pan generously and heat over medium heat. A little mixture should sizzle steadily when added.
Spoon portions into the pan and flatten to approximately 7–8 cm wide and 1 cm thick. Fry in batches without crowding, allowing approximately 3–4 minutes per side, until golden and cooked through. Let the underside set before turning. Reduce the heat if the outside browns too quickly.
Transfer the cooked fritters to a wire rack while you finish the remaining batches, adding more oil to the pan as needed. Avoid stacking until serving.