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Preheat oven to 325. Bring chicken broth to a boil.
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In a large bowl, combine rolled oats, oil, and broth. Let stand 10 minutes.
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Thoroughly stir in cornmeal, milk, cheese, and egg. Add flour, 1 cup at a time, until mixture forms a stiff dough.
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Knead dough on a lightly floured surface, mixing in additional flour if necessary. When dough is smooth, roll it to 1/2-inch thickness. Cut out bone-shaped treats with a cookie cutter and place them one inch apart on parchment-covered cookie sheets.
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Bake 40 minutes, or until golden brown. Cool completely before serving or packaging.