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Preheat oven to 425°F/215°C.
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In a large mixing bowl, combine the flour, baking soda, salt and baking powder.
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Add the cheeses, ham, and chives to the dry mixture and combine thoroughly.
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Make a well in the center of the dry ingredients, and pour the butter and buttermilk into the well.
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With clean hands, combine the ingredients until the dry mixture is moistened, do not knead.
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Turn the mixture onto a floured surface and gather the dough together.
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Gently pat the dough to make a disk about 1 ½ inches thick.
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Using a 3 inch biscuit cutter, cut as many scones as you can and lay them on a nonstick, parchment lined baking sheet.
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Gather the remaining dough lightly and cut out more scones, making sure you are gentle, do not knead.
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Bake the scones for about 12 minutes or until lightly browned.
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Serve with scrambled eggs and jam, if desired.