Heat the oven to 200°C/180°C fan/gas 6. Sift the 150g plain flour into a large mixing bowl and stir in the cornmeal/polenta, salt, baking powder, sugar, mustard powder, cayenne, 150g of the grated cheese, the chilli and the sliced spring onions. Make a well in the centre.
In a jug, mix the melted butter with the buttermilk, eggs and olive oil and pour into the well. Stir quickly to combine, then pour into the cake tin. Sprinkle with the rest of the cheese, then bake for 25-30 minutes until golden and a skewer pushed into the middle comes out clean.
Meanwhile, fry the spring onions. Fill a heavy-based deep pan with 6-8cm oil, then put over a medium heat until it reads 180°C on a digital probe thermometer (or a cube of bread turns golden in 30-40 seconds). Line a baking tray with kitchen paper and set aside.
In a wide shallow bowl mix the flour, mustard powder, garlic salt, cayenne pepper and a good pinch of salt. Beat the 2 eggs and put in another bowl, then put the cornmeal/polenta in a third similar bowl. Dust the spring onions all over in the seasoned flour, then coat in the egg, then finally toss in the cornmeal/polenta to coat.
Working in batches, fry the spring onions until golden brown (3-4 minutes), then scoop out with a wire basket or tongs and lay on the prepared tray. Immediately sprinkle with lime juice, lime zest and salt. Cook the rest of the onions.
Mix all the mayonnaise ingredients in a small bowl and season to taste. Once the cornbread is cooked, top with the crispy onions with the mayo alongside for dipping.