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Make dough: Pulse together flour, baking powder, and salt in a food processor until well mixed. Add butter and pulse until mixture resembles coarse meal. (Alternatively, whisk together dry ingredients and cut in butter with a pastry blender.) Transfer to a bowl and stir in yogurt and dill until the mixture forms a dough. Divide dough into quarters, wrapping each in plastic wrap. Chill 10 minutes.
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Preheat oven to 350°F.
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Roll out dough: Divide 1 dough quarter into 6 equal portions and form each into a 4-inch log with your hands. With a floured rolling pin, roll out each log into a 12- to 14-inch strip on a lightly floured surface. Transfer strips to 2 greased baking sheets.
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Bake crackers: Bake in upper and lower thirds of oven, switching position of sheets halfway through baking, 14-18 minutes total, or until crackers are crisp and a little bit brown. Transfer to racks to cool. Make more crackers in same manner.
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You can make crackers 1 week ahead and keep in an airtight container at room temperature.