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Heat oven to 450 degrees F. Line baking sheet with parchment.
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Combine the flour, baking powder, salt, and sugar in the bowl of an electric mixer fitted with the paddle attachment.
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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.
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Turn the dough onto a lightly floured work surface and knead until top surface is smooth.
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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.
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Place biscuits on parchment lined baking sheet one inch apart.
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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.