In a mixing bowl, whisk together the eggs and caster sugar until well combined. Gradually add in 1 cup of the whole milk and the melted butter, mixing until smooth.
In a separate bowl, sift together the all-purpose flour, baking soda, and cream of tartar.
Gradually fold the dry ingredients into the wet mixture, alternating with the remaining 1/2 cup of milk. Be careful not to overmix; a few lumps are okay!
Place a non-stick skillet or griddle over medium heat. Allow it to warm up before adding a small amount of butter to coat the surface evenly.
Spoon about 1/4 cup of batter onto the skillet for each scone. Cook until bubbles form on the surface (about 2-3 minutes), then flip and cook for an additional 2 minutes, or until golden brown.
Transfer the cooked scones to a cooling rack for a moment, then serve warm with your favorite toppings such as butter, jam, or clotted cream.