Heat oven to 375° F. Whisk together milk and eggs. In separate bowl, mix flour, cornmeal, sugar, baking powder, and butter. Add milk-egg mixture and stir. Spoon mixture into muffin cases cups.
Cut cheese into cubes and press down into mixture. Bake in center of oven about 15 minutes.
To make Nut Pesto: In blender or using hand blender, combine olive oil, parsley, garlic, walnuts, cashews, salt, and pepper. Pulse or blend until coarsely chopped.
Serve corn muffins with additional cheese, Nut Pesto, and thin slices of cured ham, if desired.
Notes: If possible, use stiff paper cups, so muffins stand up better. Cornbread can also be baked in large, round baking pan, about 8 inches in diameter; adjust baking time as needed until done.