Take a mixing bowl and add water, eggs, oil, peanut butter and vanilla in it. Mix the ingredients with the help of a wire whisk until a thick paste is formed. Now add cornmeal, flour and oats to same mixture. Stir these ingredients with a whisker until everything is incorporated well and a dough is formed.
Make sure that the work surface is clean and sprinkle flour on it. Knead the flour, adding more of it as required to form a dough which is flexible. The thickness of the dough should be around ¾ inch so that the biscuits are of perfect crispness and also chewy. You can either use your hands to shape pieces of the dough like you want, or bone shapes can be cut out of the dough using a cutter.
Take a baking sheet which is not greased and place the cookies on the tray before putting them in the oven. Set the oven to 400 degrees and the timer to 25 minutes. The biscuits will bake in 20 to 25 minutes, depending on how thick they are. If you want them to be more crispy, you can turn the oven off and leave them in it for a few more minutes. Once they are done, you should store them in an airtight jar so they last long.