Place chicken into a ziplock bag. Add Brussels sprouts, olive oil, vinegar, minced garlic, salt, and pepper. Seal and gently toss to coat. Pour contents into slow cooker; cover and cook on low for 8 hours.

Approximately 30 minutes before chicken is done cooking, peel potatoes and cut into quarters. Place into a large pot of boiling water along with broccoli. Boil for 15 minutes until fork tender, then drain, add butter, and mash together. Gradually add milk until desired consistency is reached; stir in Parmesan cheese.

Serve chicken with potatoes, Brussels, and watermelon on the side.