Preheat Oven: Preheat your oven to 350°F. Grease a muffin tin or line it with paper muffin cups.
Dry Ingredients: In a medium bowl, combine the flour, cornmeal, baking powder, salt, and sugar. Stir in ¼ cup of the grated cheddar cheese.
Wet Ingredients: In a separate bowl or measuring jug, whisk together the melted butter, milk, and vegetable oil. Add the slightly beaten eggs and whisk until well combined.
Combine Mixtures: Gradually add the wet ingredients to the dry ingredients, mixing gently with a fork until just combined. The batter should be slightly airy and sticky.
Fill Muffin Tin: Spoon the batter into the prepared muffin tin, filling each cup about two-thirds full.
Add Toppings: Sprinkle the remaining ¼ cup of grated cheddar cheese on top of each muffin and place a couple of jalapeño slices on each.
Bake: Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out with a few crumbs attached.
Cool: Allow the muffins to cool in the tin for a few minutes before transferring them to a wire rack to cool completely.