Preheat the oven to 350°F. Line a baking sheet with parchment paper or a silicone mat.
Peel and cut the apple into small pieces.
In a large bowl, stir together the apple pieces, cheese, and egg.
Stir in the flour and enough water as needed to make a rollable dough.
Place the dough on parchment paper. Use a rolling pin to roll the dough out to about 1/4-inch thick.
Use a cookie cutter to cut out as many treats as possible. Gather the scraps, re-roll, and cut.
Place the cutouts on the lined baking sheet. Bake for 18-20 minutes.
Allow the treats to cool completely on the baking sheet.
Store the treats in an airtight container in the fridge.