Place chicken breasts in a 2-quart saucepan with water. Cover and cook on medium-high for 20-30 minutes until chicken is tender and fully cooked. Shred with two forks, then add onion and ketchup. Heat for a few minutes more.
For the Homemade Ketchup:
Combine all ingredients in medium saucepan and bring to a boil. Turn down heat, then cover and simmer for 30 minutes.
Puree with an immersion blender, then cook uncovered for up to an hour more (or until thickened).
For the Apple Slaw:
Toss apple matchsticks in lemon juice to coat. In a separate bowl, add remaining four ingredients and whisk to combine to make the dressing. Then drizzle over apples and stir.
To assemble the cones:
Once your cone is ready, fill with a scoop of mashed potatoes to seal up the hole in the bottom. Then add a scoop of Apple Slaw, followed by the Pulled Chicken on top. Enjoy!