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Preheat oven to 425°F. Line a baking sheet with parchment paper.
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In a large bowl, whisk together flour, baking powder, salt, and a pinch of sugar.
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Cut cold butter into small cubes and add to flour. Work butter into flour until it resembles coarse cornmeal.
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Create a well in the center and pour in cold buttermilk. Stir gently until dough just comes together.
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Turn dough onto a lightly floured surface and knead gently 3-4 times until just cohesive.
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Roll out dough to about 1/2 inch thickness. Using bunny-shaped cookie cutters, cut out shapes.
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Place biscuits on prepared baking sheet about 2 inches apart. Brush tops lightly with buttermilk.
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Bake 12-15 minutes until golden brown on top. Biscuits should be tender and fluffy inside.
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While biscuits bake, prepare ham salad: mix diced ham, celery, pickles, and mayonnaise. Season with salt, pepper, and dill.
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Remove biscuits from oven and let cool 2 minutes. Split biscuits and fill with ham salad.
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Serve immediately on a platter. Store biscuits and ham salad separately if making ahead.
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Unfilled biscuits keep 1 day at room temperature and freeze beautifully up to 3 months.