Chicken n' Dumplings is a down-home recipe. The perfect comfort food.
Melt the butter in a large saucepan. Add the onions, celery, carrots and peppers. Saute for 3 minutes, until the vegetables have softened and the onions are translucent. Add the minced garlic and cook for an additional minute. Add the cooked chicken and diced potatoes.
Sprinkle the flour over the top and cook for an additional minute, gently tossing to work in the flour. Let it cook for 3 minutes. Pour in the chicken broth and cream of chicken soup. Add 1/2 tsp dried thyme, & 1/2 tsp dried rosemary.
Pour in the evaporated milk and increase heat until it reaches a soft bubble. Decrease heat to medium low. Let it simmer, partially covered, until the potatoes are fork tender. Stir in frozen broccoli florets. Remove from heat. Season with salt and pepper.
Combine the Bisquick, milk, and egg until well-combined. Pour it over the filling. DO NOT do this step ahead of time. Wait until the last minute before pouring the batter on the top for the best 'rise'