Pre-heat oven at 350 degrees F. Line a muffin tray with liners.
Grate the zucchini. And using a kitchen towel, squeeze out all the moisture. This is a key step to ensure your muffins don't turn out too mushy. So don't skip this step.
In a small bowl, mix the melted butter and chives. In a larger bowl, mix the eggs and milk. Then add the butter and chives mix. Fold in the cheese, ham and zucchini.
In another bowl, whisk the flour, baking powder and salt. Then combine the dry ingredients into the wet ingredients. Gently mix them together, careful not to overmix.
Scoop the muffin batter into the tin, about 2/3 full. You can top with more cheese if you like. Bake for 20-25 minutes or until golden on top. Serve warm or store in the fridge for up to 5 days, or in the freezer for up to a month.