Pour in the chicken broth. Add thyme, rosemary, salt, and pepper. Stir gently.
Secure the lid and set the valve to Sealing. Cook on High Pressure for 8 minutes.
When the cooking cycle finishes, perform a Quick Release (QR) of the pressure.
Remove the chicken and shred it using two forks. Return the shredded chicken to the pot.
In a small bowl, whisk together the 1/2 cup flour and 1/2 cup cold water until smooth to create a slurry. Pour the slurry into the simmering liquid in the pot and stir until the broth thickens slightly.
For the dumplings, whisk together the 2 cups flour, baking powder, and salt in a medium bowl.
In a separate small bowl, mix the milk and melted butter. Pour the wet ingredients into the dry ingredients and stir just until combined; do not overmix.
Drop spoonfuls of the dumpling batter directly onto the surface of the simmering stew in the pot, leaving space between them. Do not stir after adding the dumplings.
Secure the lid again and set the valve to Sealing. Cook on High Pressure for 5 minutes.
Once finished, perform a Natural Pressure Release (NPR) for 10 minutes, then carefully Quick Release any remaining pressure. Serve immediately.
Notes
If you prefer a richer flavor, use chicken thighs instead of breasts.
For a thicker stew, increase the slurry to 3/4 cup flour mixed with 3/4 cup cold water.
You can use pre-shredded rotisserie chicken to skip the initial pressure cooking step for the chicken; adjust the cooking time accordingly.