Combine flour, cornmeal, baking powder and salt in a medium bowl.
In a large bowl, cream together butter and sugar with an electric hand mixer.
Add milk and oil and mix on low. Add two slightly beaten eggs to the mixture and whisk or lightly beat to incorporate.
Slowly add the cornmeal mixture in; mixing the two together with a fork until combined. The batter should be slightly airy and sticky.
Spoon into a greased muffin tin and bake for 18-20 minutes at 350F, using a toothpick to test the center of the muffins for doneness.
Allow to cool. Of course typical cooling protocol in this household involves munching a molten hot muffin while the others chill to room temperature.