Heat oven to 450 degrees F. Line baking sheet with parchment.
Combine the flour, baking powder, salt, and sugar in the bowl of an electric mixer fitted with the paddle attachment.
Add the butter and mix on low speed until the butter is the size of peas. With the mixer on low, add the half-and-half and beat until just mixed. Add the chives, parmesan cheese and mix until just combined.
Turn the dough onto a lightly floured work surface and knead until top surface is smooth.
Shape dough into a rectangle and using a rolling pin, roll dough to 3/4 inch thickness. Use a knife or a metal bench scraper and cut into 2 1/2 inch squares.
Place biscuits on parchment lined baking sheet one inch apart.
Brush tops with melted butter and bake at 450 degrees F for about 12-14 minutes or until tops are golden brown. Remove from oven and cool on a wire rack for five minutes.