Preheat the oven to 375 degrees. Line a muffin tin with paper liners or grease well with oil.
Cut the hot dogs in half lengthwise then across into 1/4-inch pieces. Measure the cup of milk then stir in the vinegar and set aside for 5 minutes. (You just made buttermilk!)
In a medium-size bowl, whisk together the cornmeal, flour, baking powder, baking soda, and salt.
In a large bowl, whisk together the eggs, oil or butter, honey, and the milk-vinegar mixture
Dump the dry ingredients into the bowl with the wet ingredients and stir to combine. Stir in the chopped hot dogs and half of the cheese, if using.
Scoop a 1/4 cup of batter into each muffin cup. Sprinkle a pinch of the remaining cheese over the top, if using.
Bake until the tops of the muffins are golden brown and a toothpick inserted into the center of the muffins comes out clean, about 15 minutes.
Enjoy the muffins warm, room temperature, or cold. (My kids like them with ketchup.) Store in an airtight container in the fridge for 3 to 4 days or individually wrap and freeze for up to 2 months.