Place an oven rack in the center of the oven and preheat to 375 degrees F. Spray a heavy baking sheet with vegetable oil cooking spray or line with a silicon baking mat. Set aside.
In a large bowl, combine the flour, oats and baking powder. Stir in the broth and peanut butter until the mixture forms a crumbly dough. Press the dough together to form a ball.
On a lightly floured work surface, knead the dough for 30 seconds until smooth. Roll out the dough into a 10-inch circle, about 1/2-inch thick. Using a bone-shape cookie cutter, cut out bones and place on the prepared baking sheet (any scraps of dough can be formed into a ball and re-rolled). Sprinkle with the Parmesan.
Bake until light golden, 20 minutes. Transfer to a wire rack and cool completely. Store in an airtight container for up to 1 week.