Melt the salted butter in a 3-quart pot over medium heat. Add the chopped onion, diced celery, and minced garlic. Sauté for about 2 minutes until the onion becomes translucent and the aromatics are fragrant. This creates a flavorful base for the filling.

Stir in the shredded rotisserie chicken, sliced carrots, frozen peas, chicken broth, kosher salt, ground black pepper, and dried thyme into the pot with the sautéed aromatics. Cook everything together for about 10 minutes, stirring occasionally, until the vegetables have softened and the flavors are well combined.

Reduce the heat to low. Pour the heavy cream in slowly, stirring constantly, then sprinkle in the shredded cheddar cheese and mix well. Allow the mixture to simmer gently for about 5 minutes until the filling is creamy and slightly thickened. I like to let it bubble a bit to develop even more flavor before moving on.

Preheat your oven to 400°F (not 4000°F as originally stated). Transfer the hot filling from Step 3 into a casserole dish. Unroll the refrigerated pie crust and lay it over the filling, trimming or tucking the edges as needed. Use a fork or pie crimper to secure the edges of the crust to the dish.

Beat the egg in a small bowl and brush it gently over the entire surface of the pie crust. Cut a few slits into the crust to allow steam to escape during baking. Place the casserole in the preheated oven and bake for 15-20 minutes, or until the crust is golden brown and flaky. For an even shinier crust, I like to do a second light coat of egg wash halfway through baking.