Heat a large Dutch oven over medium-high heat. Once hot, add the olive oil and swirl to coat the bottom. Place the chicken cubes in the bottom, and cook for 6 minutes, stirring occasionally. Remove the chicken from the pot, and set aside.
Turn the heat to medium, and add in the butter. Once the butter has melted, add in the onion and carrots. Sauté for about 3 minutes, or until the onions are just starting to turn translucent. Add in the garlic and stir. Sauté for another minute, or until aromatic.
Sprinkle in the flour and stir until the butter and flour are well combined (making sure no large lumps form). Add the chicken and its juices back into the pot. Mix so that the chicken gets coated in the flour mixture.
Mix together the chicken broth and milk in a large liquid measuring cup. Slowly pour in the chicken broth and milk mixture while stirring. Sprinkle in the dried thyme, parsley, black pepper, and sea salt. Stir to mix. Turn the heat up to medium-high, and bring to a gentle boil.
When the soup has come to a rapid simmer add in the frozen peas and cook for 10 minutes. After the soup has simmered rapidly for 10 minutes, turn the heat down to medium-low.
In a medium mixing bowl, mix the Bisquick and milk together until a dough is formed. Be careful not to over-mix the dough - that will cause the dumplings to be too dense and not cook properly. You want to stop mixing as soon as a soft dough has formed.
Use a Tablespoon to scoop out the dough and carefully drop each dough ball into the soup (make sure to only drop a dough ball where liquid is visible, you don’t want to drop dough balls on top of each other).
Place the lid on the Dutch oven, and simmer the dumplings for 20 minutes. Don’t open the lid to see if the dumplings are cooked during this time (you’ll release all the steam if you do). After 20 minutes, use a toothpick to check the center of a dumpling to see if it’s cooked through. If it’s not fully cooked, cover the pot and cook for an additional 5 to 10 minutes.
Once the dumplings are cooked through, carefully taste the soup and adjust salt to taste. If the soup is thicker than you’d like, stir in some additional chicken broth, milk, or some cream if you’d like it really creamy.
Garnish with fresh parsley, and serve.