Pre-heat oven to 350ºF and grease muffin tins with a spray oil to give a light coating.
Place dry ingredients in a mixing bowl and whisk lightly with a balloon whisk to aerate and ensure well combined. Add grated veggies, ham and cheese. Using your fingers, lightly toss and mix through to separate and evenly distribute ingredients.
In a different bowl, whisk together milk, egg and oil. Add wet ingredients to dry. Stir lightly until just combined – do not overwork or muffins will toughen.
Spoon mixture into prepared muffin tins. Cook for 15 mins for mini muffins and 25 mins for the larger ones.
Allow to cool in tin for 5 mins before removing to a cooking rack. Eat immediately or keep them in the fridge for a few days, giving them a quick zap in the microwave to freshen them. Alternatively, freeze in freezer bags and enjoy whenever.