Combine. Place carrots, celery, and onion into the bottom of a 4-6 quart slow cooker. Add mushrooms on top of the other vegetables. Sprinkle with a little of the salt. Place chicken breast on top of the veggies. Sprinkle chicken with garlic powder, remaining salt, the pepper, and the thyme.
Make Flour Slurry. In a small bowl, whisk together the flour and water. Pour over chicken and vegetables. Top with chicken broth and stir to combine. Slow Cook. Cook on LOW for 4-5 hours (or on HIGH 2-3 hours) or until chicken is tender.
Cook Puff Pastry. Preheat oven to 425 degrees F. About 15 minutes before serving, fold the puff pastry into thirds (it's usually packaged like this anyway, just don't unfold it). Slice puff pastry into 4 pieces. (If you're feeling fancy, you can cut it into fancy shapes.) Place on a baking sheet covered with parchment paper or sprayed with nonstick spray. In a small bowl or cup, beat egg with a fork. Brush egg over the tops of the puff pastry. Bake at 425 degrees 8-10 minutes or until golden brown.
Finish Pot Pie. While the puff pastry bakes, shred or dice chicken and return to the slow-cooker. Stir in cream or half-and-half and frozen peas. Taste and add additional salt and pepper to taste. Heat through until warm.
Serve & Store. Divide chicken mixture among four bowls and top each with a puff pastry square. enjoy warm! Store leftover chicken pot pie filling in an airtight container in the fridge 2-3 days. Store leftover puff pastry squares in a bag at room temperature 2-3 days.