First you open the cooking object via the UI prompts shown below.
Place one fuel item and one cookable item inside the cooking objects storage slots.
Ignite the fire and watch the cooking objects cook. (Yes I replaced the wood with leafs)
Now you have some crisp and well cooked meat. Delicious!
I feel like once this new system is learned by players that it will be easier to use and manage. The extra slots make cooking a bit more realistic/manageable as well.