Combine flour, 2 tsp paprika and salt. Coat chicken pieces with flour mixture (be sure to cut breasts in chunks so they absorb lots of moisture/gravy).
In a Dutch oven, heat the butter and olive oil over med-high heat. (Butter adds unbeatable flavor to the gravy, so just do it, book some time on the treadmill later.) Brown chicken on both sides. Remove chicken and set aside.
Add broth, chicken, remaining paprika and chopped fresh thyme. Cover and simmer gently for 45 minutes or until chicken juices run clear. Remove chicken and keep warm in oven.
For dumplings, combine flour, baking powder and salt. Beat egg and milk, stir into flour mixture and mix well. Drop dough (it'll be sticky) 1 tablespoon at a time into simmering broth. Cover and simmer for 10 minutes. Remove dumplings and keep warm in oven with chicken while you thicken your gravy.
For gravy, add milk or cream to broth (if you would like a creamy gravy), then combine cornstarch and water together, and stir into broth. Bring to a boil, cook for 2 minutes. Reduce heat, reintroduce your chicken and dumplings into your yummy gravy and enjoy!