Preheat oven to 400 degrees. Spray a 9x9 baking pan with cooking spray.
In a medium sized bowl, whisk together cornmeal, baking powder, thyme, oregano, sugar, pepper, and salt. Then, stir in chicken broth until well combined.
Pour mixture into prepared baking pan (mixture is very liquid, but it does firm up in the oven). Bake until top is golden brown, 33-34 minutes.
Let cool for 30 minutes in pan, then turn pan over on cutting board. Transfer cake/cutting board to refrigerator for at least 1 hour.
After cake has cooled, cut into 9, 3-inch squares.
Heat ~1 tablespoon of corn oil into pan over medium-high heat. Add as many cakes as you can fit into pan without the cakes touching. Let cook until side down is lightly browned, about 2 minutes. Flip and repeat for other side.
Remove cakes from pan and repeat with remaining cakes, adding oil as needed in pan.