Pat chicken dry with paper towels and season with salt and pepper. Heat 1 Tbsp oil in a deep 12 inch skillet (or dutch oven) until very hot, over medium-high heat. Brown half the chicken, on each side, about 4 minutes per side, and transfer chicken to slow cooker. Repeat with another 1 Tbsp oil and remaining chicken.
Heat remaining oil in the now empty skillet. Add onion and cook until softened and lightly browned, about 5-6 minutes. Stir in tomato paste, garlic and thyme and cook until garlic is fragrant, about 30 seconds to 1 minute. Quickly stir in flour and cook about 1 more minute. Slowly whisk in wine first, then 2 cups of broth, scraping up any browned bits and removing any lumps. Stir in potatoes and carrots and bring to a simmer. Cover, reduce heat to medium-low, and simmer just until vegetables begin to soften on the edges, but are not cooked through, about 10 minutes. Transfer mixture to slow cooker, on top of chicken.
Stir remaining 2 cups of broth and bay leaves into the slow cooker. Cover, and cook on LOW for about 4 hours, until chicken is tender and cooked through.
Transfer chicken to a cutting board, and shred into large chunks using 2 forks. Discard bay leaves.
Add chicken back into slow cooker and add the peas. Stir, and then leave until heated through and peas are cooked, about 5-10 minutes. Stir in parsley if using, and add salt and pepper to taste. Serve hot.
Enjoy!