Combine all the ingredients for the batter in a large bowl, mixing well but not worrying about any lumps that may have formed. Cover and chill while you prepare the vegetables.
Cut the cauliflower and broccoli into small florets. Core and deseed the pepper, then cut it lengthways into 8 strips. Slice the courgette into 1 cm (½ inch) rounds and cut the onion into 8 wedges. Tip the flour into a bowl and season with salt and pepper, then toss in the prepared vegetables.
Heat enough oil for deep-frying in a deep saucepan to 180–190°C (350–375°F), or until a cube of bread browns in 30 seconds. Take 5 or 6 vegetable pieces from the flour, shake off any excess, then plunge into the batter. Lift out, letting the batter drip off slightly, then carefully plunge into the hot oil. Cook for about 3 minutes until golden. Remove with a slotted spoon and drain on kitchen paper. Once all the vegetables are cooked, lightly dust the parsley sprigs with flour, dip in the batter and cook for 1–2 minutes, or until just golden.
Season the vegetables and parsley with salt and serve immediately.