Heat the oven to 190C/170C fan/gas 5. Butter a 30cm ovenproof pan. Combine the semolina, flour, baking powder and bicarb in a large bowl and season. Put the butter, eggs, pumpkin, buttermilk and chillies in a jug and whisk until combined. Gradually stir the wet ingredients into the dry, being careful not to over-mix. Pour into the pan and bake for 50 mins-1 hr until golden.
Meanwhile, prepare the whipped jalapeño butter. Beat the butter with the jalapeños and the liquid from the jar using an electric whisk, until the mixture has turned light and pale. Season to taste.
Once the cornbread is cooked, serve warm or leave to cool, with the jalapeño butter on the side to spread over. The cornbread will keep in an airtight container for up to three days, or frozen for two-three months. The butter will keep in the fridge, covered, for up to one week.