Preheat your oven to 425℉.
In a large bowl mix together the flour, baking powder, and salt.
To the flour mixture, gently mix in the butter until combined. Do this gently - you don't want huge butter clumps, you want it to stay relatively grated in size.
To the same mixture, gently mix in the cheddar and chives until combined.
In a measuring cup or small bowl, mix together the honey and buttermilk. The honey may clump up a little but but mix it into the buttermilk best you can (I found this pretty easy when using a fork).
Add the buttermilk honey mixture into the bowl with the flour mixture. Gently stir with a wooden spoon until it just starts to come together. Then pour it out onto a floured surface.
Carefully work the mixture together with your hands until a dough forms. It'll be a bit sticky, but if it seems overly sticky then sprinkle some more flour on. Flatten it out to about 1" and then fold the sides into each other. Flatten it out again and fold the sides over once more. Then do a final flattening to 1" thick.
Using your biscuit cutter, go straight down and straight back up in the dough as many times as you can (do not turn the cutter, this will prevent it from rising properly). Form the scraps back into a 1" thick disk and repeat - you should be able to get 10 biscuits total.
Transfer the biscuits to a parchment-lined baking sheet about ¼ inch apart and brush the tops of the biscuits with melted butter.
Bake at 425℉ for 20-25 minutes until golden.