Heat the oil in a frying pan (roughy 20cm wide) and heat the grill to high. Season the eggs and add to the pan along with the peas. Quickly mix, then leave for 8 mins over a low-medium heat until the underside is set and just turning golden. Scatter over the cheese and grill for 3 mins until the surface is set and the cheese is bubbling.
Meanwhile, spread each burger bun with chutney or chilli jam. Cut the omelette into 4 wedges and sandwich between the buns, add a handful of leaves and a few slices of tomato, and serve with sweet potato wedges, if you like.