Preheat the oven at 425 °F (220 °C). Line a muffin tin with paper cups.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, and pepper. Incorporate the ham and shredded cheese. Pour in the milk and mayonnaise and stir with a spoon until all ingredients are wet.
Fill the muffin cups with spoonfuls of wet dough. Bake for 15 to 20 minutes, until a toothpick poked in a muffin comes out clean.
The muffins are best enjoyed still warm, when the cheese is soft, but also make a convenient picnic item once cold.
This recipe relies on a flavorful cheese being used, but if you substitute de gouda for a plainer mozzarella, for example, then feel free to season with the spices or herbs of your preference.
The buttermilk can be replaced with 4/5 cup (20 cl) of milk + 1/5 cup (5 cl) of lemon juice.