Slow cooker method: Add all ingredients, except peas, parsley, and olive oil, to the slow cooker. Use just enough water to cover ingredients. Cover and cook on low 6 to 8 hours or high 4 to 5 hours. About 15 minutes before turning off the slow cooker, add peas and parsley.
Stove top method: Add all ingredients, except peas, parsley, and olive oil, in a large pot. Use enough water to cover ingredients. Bring to a boil and reduce to a simmer. Cover and cook on low 1 hour or until carrots are tender and chicken cook through. About 15 minutes before turning off, add peas and parsley,
Allow ingredients to cool slightly. Using a slotted spoon, add ingredients, and olive oil to a mixing bowl and either, mash with a fork, potato masher, or use a food processor, depending on the consistency preferred. I like to use a food processor and pulse about 3 to 4 times so that it's the consistency of canned dog food. Allow to cool completely before dividing into freezer safe ziplock bags or containers.
MAKE-AHEAD: The dog food mixture can be divided up and stored in individual freezer safe ziplock bags. Frozen baggies should be defrosted in the fridge overnight. The serving size will depend on the size and breed of your dog. If you're unsure of how much to feed your dog, check with your vet first.