Cut roast into quarters; set aside.
Add flour, salt, and pepper to a small bowl and stir to combine. Use mixture to coat roast on all sides.
Slice onion and mince garlic; add to slow cooker along with brown sugar, bay leaves, and broth. Mix to combine. Add beef. Cover and cook on low for 8 hours.
Before beef is done, peel and boil potatoes until fork tender. Drain. Add milk and butter, and mash until smooth. While potatoes are boiling, steam broccoli.
Serve beef with broccoli, mashed potatoes, and sliced apples on the side.