1. Preheat oven to 425°F. Line 2 large baking sheets with parchment.
2. In a large bowl, combine flour, salt and baking powder and mix well. Add cold butter, cheese and chives. Use a pastry blender, 2 knives or fingertips to mix in butter until mixture is crumbly, with a few pea-size pieces of butter or cheese remaining. Add milk and gently mix to moisten, no more than 10 seconds. Dough will be rough; do not overwork.
3. Turn dough out onto a large floured work surface and knead gently into a ball, no more than 6 to 8 quick turns. Working quickly, roll dough out into a 1/2-inch-thick circle. Cut out small biscuits using a 1-inch cookie cutter. Gather scraps of dough, roll out again to 1/2-inch thickness and cut out more biscuits. Place biscuits about 1 inch apart on baking sheets. Lightly brush tops of biscuits with melted butter, if desired. Bake until lightly browned on top, 15 to 18 minutes. Serve warm.