Step 1

Pour the olive oil into a multi-functional pressure cooker (such as an Instant Pot®) and select the Saute function. Cook onion, carrot, celery, and bay leaf until the vegetables are soft and the onion has turned translucent, about 5 minutes.

Step 2

Add chicken broth, chicken thighs, chicken breasts, thyme, marjoram, salt, and pepper. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 9 minutes. Allow 10 to 15 minutes for pressure to build.

Step 3

Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Carefully remove the chicken pieces with tongs and place them in a bowl to cool slightly; discard bay leaf.

Step 4

Mash butter with the flour to make a smooth paste; set aside.

Step 5

Combine flour, baking powder, and salt in a bowl for the dumplings. Cut in cold butter until mixture is the texture of cornmeal. Stir in parsley and set aside.

Step 6

Shred cooled chicken and return to the pot. Taste the broth and adjust the seasoning if needed. Add peas and green beans. Stir in the flour-butter paste. Select Saute function to bring broth back to a boil.

Step 7

Pour buttermilk into the dumpling mixture and stir until combined. Drop the dumpling dough by heaping spoonfuls on top of the stew; a small cookie scoop works well.

Step 8

Cover pot with the lid, leaving the steam vent open. Select Slow Cooker function and simmer on Low, covered, until dumplings are cooked through, 10 to 12 minutes. A skewer inserted in the center of a dumpling should come out clean.