Heat oven to 400°F. Line a 12-cup muffin pan or lightly grease.
Whisk cornmeal, flour, baking powder, baking soda, salt, and sugar in a large bowl.
In another bowl, whisk buttermilk, honey, melted butter, oil, eggs, and vanilla until smooth.
Pour wet ingredients into dry. Stir gently until just combined; a few small lumps are fine.
Divide batter among cups, filling each about three-quarters full.
Bake 12 to 15 minutes, until tops are golden and a toothpick comes out clean.
Cool in pan 5 minutes, then move muffins to a rack to finish cooling.