Grease and line a standard 12 hole muffin tin with muffin cases.
Preheat oven to 180 degrees (160 degrees if using fan forced).
Whisk together the buttermilk, oil and eggs in a bowl and set aside.
Sift the self raising flour into a large bowl.
Add the grated cheese, ham, grated zucchini, sea salt and pepper.
Mix to combine.
Pour the buttermilk mixture over the top of the flour mix and stir gently.
Mix until only just combined (over-mixing will lead to tough muffins!).
Divide the mixture equally between the muffin cases.
Bake in the oven for approximately 15 minutes or until cooked through (test with a skewer).
Leave the muffins in the pan to cool slightly, before placing onto a wire rack to cool completely.