Preheat oven to 350 degrees Fahrenheit. Lightly grease baking sheets, or line them with parchment paper.
Wisk the flour and baking powder together and stir in the turkey and dried cranberries. Make a well in the center of the mixture, and drop the egg into the center. Pour in the olive oil and about 1/2 of the chicken broth. Gradually add more chicken both until the consistency of the dough is soft and moist.
Knead the dough on a floured work surface for 1 to 2 minutes. Roll the dough out 1/4 inch thick, and cut out with your favorite pet or holiday themed cookie cutters.
Bake until the treats turn brown (about 25 minutes) or until nice and crisp.