Prepare the Chicken Stew:
Heat olive oil in a large pot or Dutch oven over medium heat.
Add diced onions and cook until translucent. Stir in minced garlic and cook for an additional minute.
Add chicken pieces to the pot and cook until no longer pink.
Stir in carrots and celery, cooking for about 5 minutes.
Sprinkle flour over the mixture and stir to coat. Cook for 1-2 minutes to eliminate the raw flour taste.
Gradually add chicken broth, stirring continuously to avoid lumps.
Bring to a boil, then reduce heat and let simmer for 20 minutes.
Stir in frozen peas, heavy cream, thyme, rosemary, salt, and pepper. Adjust seasoning to taste.
Make the Dumplings:
In a large mixing bowl, whisk together flour, baking powder, salt, and sugar.
Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Pour in milk and stir until just combined. Do not overmix.
Cook the Dumplings:
Drop spoonfuls of the dumpling batter onto the simmering chicken stew. Be careful not to overcrowd.
Cover the pot with a lid and let simmer for 15-20 minutes, or until the dumplings are puffed up and cooked through. Avoid lifting the lid during this time.