Pulse cheese in a food processor until finely ground, then transfer to a bowl.
Whisk in flour, baking powder, and salt, then blend in butter with your fingertips or a pastry blender until mixture resembles coarse meal.
Form a well in center of flour mixture and add milk and egg, then stir with a wooden spoon until a dough forms.
Gently knead dough on a lightly floured surface until smooth, about 2 minutes. Chill dough in a sealed plastic bag, 1 hour.
Put oven racks in upper and lower thirds of oven and preheat oven to 350°F.
Divide dough in half and roll out into 2 (12-inch) rounds (less than 1/16 inch thick) on a lightly floured surface with a lightly floured rolling pin.
Cut out as many crackers as possible from dough with cutters and transfer to 2 large baking sheets, arranging crackers about 1/4 inch apart. Discard remaining dough. (Do not reroll scraps; crackers would be tough.)
Bake crackers, switching position of sheets and rotating them 180 degrees halfway through baking, until undersides are golden, 10 to 12 minutes. (Crackers positioned near edges of pan may need to be removed first.) Cool crackers completely on sheets on a rack, about 15 minutes.
*Available at foosecookiecutters.com.
• Dough can be chilled in sealed plastic bag up to 1 day.• If you can't find animal-shaped cutters, dough can be cut into shapes with a sharp knife.• Crackers keep in an airtight container at room temperature 3 weeks.*Available at foosecookiecutters.com.
