In a dutch oven or medium soup pot, melt butter over medium heat. Add onions and carrots and cook until onion softens, about 4-5 minutes.
Add flour and 1/2 teaspoon salt. Stir continuously until mixture has a nutty aroma and is a pale golden brown color, about 3-4 minutes.
Pour in the broth and whisk constantly. Bring to a boil and continue stirring until mixture thickens, about 5-6 minutes.
Preheat oven to 375 degrees.
Let mixture cook and simmer for 10 minutes.
Stir in chicken, peas, and thyme. Season with salt and pepper.
Pour chicken sauce into a casserole dish.
Cut vents in puff pastry, then place over the top of the casserole dish.
Brush the puff pastry with egg yolk.
Cook for 45 minutes or until the sauce is bubbling and the crust is golden brown.