Preheat the oven to 325 degrees F.
In a medium bowl, whisk together eggs, olive oil, and water until the mixture is thick and frothy (approx. 1 – 2 minutes). Fold in the cheese.
Add the flour, a half cup at a time, stirring to combine, until you reach 1 1/2 cups. When the dough becomes too stiff to stir, continue adding flour 1 tablespoon at a time, knead it in with your hands. As the warmth from your hands works the dough, the cheese will melt and smooth out the dough.
If the mixture remains slightly crumbly even after you have kneaded it for several minutes, rinse your hands with cold water, shake them off and work this small amount of water into the dough – that should be just enough to bring it together perfectly.
Using a rolling pin, roll out your dough to ¼” thick. Use a cookie cutter to cut the dough into shapes.
Place the dough on a cookie sheet; the dough will have very minimal spread, so the cookies do not need much extra spacing.
Bake your dog treats for 17 – 20 minutes until the bottoms are lightly golden.
Allow the dog treats to sit on the baking sheet for 2 minutes after you’ve taken them out of the oven, then move them to a wire rack to cool completely.
For a crisper, crunchier treat, turn off the oven and allow the treats to cool inside overnight.
Store in an airtight container for up to a week or in the freezer for up to 3 months.