In a medium mixing bowl add smaller amount of flour (1½ cup), baking powder (1 tbsp), baking soda (¼ tsp), and salt, (1 tsp) & whisk together.
Grate the 1/2 cup very cold butter on top of the flour mixture, and mix in with fingers, mixture should be crumbly. You could cut in cubes, but grating is way easier.
Add sourdough discard to the bowl and mix until shaggy dough forms.
Add chopped chives(1/4-1/2 cup) and grated cheddar cheese (1/2 cup), and mix.
Gather dough with hands and press together, if dough is very sticky, add the rest of your flour ¼ cup at a time.
Once dough has come together, and chives and cheddar are evenly mixed in, bring dough out onto a floured surface.
With a well floured rolling pin, roll dough out to about ½ inch thick & sprinkle a thin layer of goat cheese crumbles on half of the dough. (If you are not using goat cheese, continue with the rolling out and layering, but skip the cheese in the layers).
Fold half without the goat cheese on it up and over the other half, flatten it out a bit with your rolling pin, this helps to secure layers together.
Again sprinkle goat cheese on half of the rolled dough, and fold the other half up and over the cheese side, roll to flatten it out a bit.
Repeat the layering with goat cheese one more time.
Gently roll dough out a bit again, fold the bottom edge up about 2/3rds of the way, and the top down to meet the bottom (In thirds like a pamphlet).
Cut into 8 biscuits, and brush with melted butter.
Preheat Oven to 425℉
Bake for 15 minutes, until golden brown.
Remove from oven and allow to cool- serve warm!