Prepare the vegetables: Dice the carrots, potatoes, and onion, and mince the garlic.
Place the chicken breasts at the bottom of the slow cooker. Layer the carrots, potatoes, peas, onion, and garlic on top.
In a mixing bowl, whisk together the chicken broth, heavy cream, thyme, rosemary, salt, pepper, and flour until well combined.
Pour the mixture over the chicken and vegetables in the slow cooker. Stir gently to combine.
Cover and cook on low for 6 hours or on high for 3 hours until the chicken is cooked through and the vegetables are tender.
Once cooked, remove the chicken breasts from the slow cooker and shred them using two forks. Return the shredded chicken to the slow cooker and stir.
Preheat the oven to 425°F (220°C). Roll out the pie crust and place it on a baking sheet.
Pour the chicken filling into a pie dish or keep it in the slow cooker for serving. Top with the pie crust, sealing the edges.
Bake for 15-20 minutes or until the crust is golden brown. Let cool for a few minutes before serving.