Heat butter in a large ovenproof pot over medium heat. Add onion, garlic, rosemary, red pepper flakes, thyme, paprika, salt, and black pepper. Cook and stir until onion is translucent, 5 to 7 minutes. Whisk in 3/4 cup flour, creating a paste; stir until paste begins to bubble, about 1 minute more. Add broth and milk; increase heat to medium-high. Bring to a rolling boil, stirring constantly, about 2 minutes. Continue stirring until sauce thickens, about 2 minutes more. Reduce heat to medium-low. Add turkey, carrots, celery, and potatoes. Cover soup and simmer for 20 minutes. Meanwhile, combine 1 1/2 cups flour, baking powder, and salt in a bowl. Use an electric mixer to cut in butter until mixture resembles coarse crumbs. Stir in milk a little at a time until dough forms. Add peas to the soup and stir. Drop dough into soup by the tablespoonful; dumplings will sink slightly. Cook, uncovered, 8 to 10 minutes. Cover and cook 8 to 10 minutes more. Let sit 5 minutes before serving.