Preheat the oven to 400° F. Grease 8 wells of a regular muffin tin, or line them with paper liners.
Mix together the flour, baking powder and salt in a large bowl. Set this aside.
Whisk together the milk, eggs, melted butter and Vegemite in a medium bowl. The Vegemite is very thick so scrape down the sides of the bowl several times to make sure it is all incorporated.
Add the liquid ingredients and the chopped chives to the bowl of dry ingredients and stir everything together with a large wooden spoon or rubber spatula: it's important not to over-mix the batter, so use the spoon or spatula to stir with big strokes that get under all the ingredients and bring it all together quickly - a few floury lumps are okay. Stir one cup of the shredded Cheddar cheese through the batter.
Divide the batter evenly between the 8 greased or lined muffin wells - they should ¾ to completely full. Sprinkle the remaining Cheddar cheese over the tops along with a little black pepper.
Place the pan in the oven and bake the muffins for 15-17 minutes. The tops should be browned, but not too dark - so watch the muffins closely during the last few minutes. A toothpick inserted in the muffins should come out clean.
Remove the pan from the oven and allow the muffins to cool in the pan for 5 minutes. Run a knife along the inside edges of the cups to release the muffins and place them on a cooling rack.
The muffins are tastiest when enjoyed warm, split open with butter spread over the insides. They can be stored at room temperature for up to 3 days - reheat them gently in a toaster oven or for a few seconds in a microwave before enjoying.
Makes 8 muffins.
Notes
Try to find Vegemite at a store near you - look in their international section, and support them for carrying diverse products. If you have no luck locally you can get some online at this link.