Place the chicken breasts in the slow cooker. Add the cubed butternut squash, green beans, diced onion, and minced garlic.
Pour in the chicken broth. Cover and cook on low for 6 hours or until the chicken is tender and the squash is soft.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
In a small bowl, whisk the heavy cream with the flour, thyme, salt, and pepper until smooth. Stir this mixture into the slow cooker.
Cover and cook on high for 20 more minutes to thicken the filling.
While the filling thickens, preheat the oven to 400°F. Cut the puff pastry into four squares and place them on a baking sheet. Brush with the beaten egg.
Bake the pastry for 12 to 15 minutes until golden and puffed.
Ladle the filling into bowls and top each serving with one piece of flaky pastry.