Whisk the flour, baking powder, and salt in a large mixing bowl.
Cut in the butter with a pastry blender or fork until coarse and crumbly.
Stir in the grated cheddar and chopped chives.
Place the bowl in the freezer for 30 minutes and up to overnight.
When ready to bake, preheat the oven to 450ºF (230ºC), with one rack in the middle and one in the lower part. Line two baking sheets with parchment paper. Set aside.
Make a well in the frozen flour mixture and pour in the milk. Using a fork, quickly mix together into a shaggy dough.
Turn the dough onto a work surface (without flour) and quickly knead 25 to 30 times. Use a rolling pin to roll the dough out to a 1-inch thickness. Cut the dough with your desired size cutter (see notes). Place the cut biscuits on the prepared baking sheets with space between each. Brush the top of each biscuit with milk and sprinkle with flaky salt (if using).
Place the trays in the preheated oven for 14 to 16 minutes, rotating the trays themselves, as well as rotating them between the racks halfway through baking. The biscuits are done when the bottoms are a medium gold color. Transfer the trays to wire racks to cool for 10 minutes before serving.
Notes
Do not use pre-grated cheese. It doesn't melt the same way as cheese you grate yourself.
If you don't want to use the frozen flour method, use frozen grated butter instead and continue with the recipe as written.
I often use different sizes of cutters for my biscuits, but I used a 3 1/16 inch (78 mm) round cutter for this post.
The thicker you roll your dough, the taller your biscuits will be. Please note that the baking time may change.
Storage
To store cheddar chive biscuits, let them cool completely before placing them in an airtight container. They can be kept at room temperature for up to 2 days.
For longer storage, cool the biscuits completely, then transfer them to a zip-top bag or airtight container. You can store them in the freezer for up to 1 month.