Add oil to a large soup pot over medium heat. Add onion and sauté for 5-6 minutes. Add garlic and continue cooking for 1-2 minutes.
Stir in celery, carrot, mushrooms, tomato paste, poultry seasoning, salt, and pepper and cook for 5-6 minutes, stirring occasionally.
Add in peas, green beans, bay leaves, vinegar and broth. Bring to a boil, then reduce heat to medium low, cover, and simmer for 15 minutes.
In a medium bowl, stir together flour, baking powder and salt. Add the butter to the flour mixture, using your hands to cut the butter into the flour until no big lumps remain. Add in the warm water and continue mixing the dumpling mixture by hand until it comes together.
Roll the dough into small balls (1- 1 ½ teaspoon in size) and drop them into the stew. Increase the heat to medium and cook for 20 minutes, until the dumplings are still soft on the outside and chewy on the inside.
Stir in navy beans and parsley and continue cooking for 2-3 minutes. Serve warm.