Set your oven to 375°F (190°C).
Spread shredded rotisserie chicken evenly in a greased 9x13-inch baking dish.
Pour melted butter over the chicken and season lightly with salt and pepper.
In a bowl, whisk together self-rising flour and milk. Slowly pour this mixture over the chicken. Do not stir.
In the same bowl, whisk chicken broth and condensed cream of chicken soup until smooth. Pour gently over the flour layer. Do not stir.
Place uncovered in the oven and bake for 45 minutes, until the top is golden and set.
Allow casserole to sit for 5–10 minutes before serving.