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Line an 8" round pan with plastic wrap.
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In a medium bowl, whisk together the flour, baking powder, salt, dry mustard, and chives.
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Cut in the cold butter until the mixture is crumbly, with some larger pieces of butter remaining.
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Add 3/4 cup of the milk, mixing until evenly moistened. The dough should hold together when lightly squeezed. If any dry spots remain in the bottom of the bowl, use the remaining milk to bring them together.
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Turn the dough out onto a lightly floured surface and fold it over three or four times. Divide the dough in half and pat one half into the bottom of the prepared pan.
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Leaving the outer 1/2" of the dough uncovered, spread the dough in the pan with whole-grain mustard.
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Sprinkle with half the cheese, again taking care to leave the outside edge bare. Place the ham on top, then sprinkle with the remaining cheese.
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Brush the outer edge of the uncovered dough with water, then pat the remaining dough into an 8" disk and place into the pan, pressing firmly around the edges to seal.
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Refrigerate the filled biscuit for 30 to 45 minutes while you preheat the oven to 375°F. Line a baking sheet with parchment.
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Flip the biscuit and pan over onto the prepared baking sheet. Lift off the pan and peel away the plastic wrap.
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Brush the top of the biscuit with milk and bake for 30 to 35 minutes, until golden brown.
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Remove from the oven and let cool on a rack for 15 minutes before slicing. Using a serrate knife, slice in wedges by drawing the knife back and forth (don't press down hard or the filling will squeeze out) to serve.
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Store any leftover biscuit, covered, in the refrigerator for up to 3 days.