Preheat oven to 350 degrees F.
Combine flour, cornmeal, baking powder, sugar and salt in a medium bowl. Add ¼ cup of the grated cheddar.
In a separate bowl or measuring jug mix the melted butter, milk and oil with a whisk. Add two slightly beaten eggs to the mixture and whisk or lightly beat to incorporate.
Slowly add the wet ingredients to the cornmeal; mixing the two together with a fork until combined. The batter should be slightly airy and sticky.
Spoon into a greased muffin tin. Top the muffins with the remaining ¼ cup of cheddar and a couple of slices of the jalapeño pepper and bake for 18-20 minutes at 350F. Use a toothpick to test the center of the muffins for doneness. The toothpick should come out with a crumb or two.
Allow to cool.
Extra muffins can be stored in an airtight container for up to four days or they can be frozen for about a month.