Set your Instant Pot to the saute setting. Add butter and melt. Add carrots, onions and celery and saute (stirring often) for 2 minutes. Add garlic and cook until fragrant, about 30 seconds.
Add broth, water, rosemary, dill, salt, pepper and bay leaves. Stir to combine.
Add chicken and turn off Instant Pot.
Place the lid on and lock. Cook on manual setting (high pressure) for 12 minutes. When finished cooking, quick release the pressure.
Once pressure has completely released, remove chicken with tongs and transfer to a platter or cutting board.
Turn off Instant Pot and set to saute setting. Add noodles and stir to combine. Cook noodles until tender (stirring occasionally), about 6 minutes.
While noodles are cooking, remove skin from chicken and discard. Remove chicken from bones and shred. Discard bones.
Add shredded chicken to your Instant Pot and stir to combine. Remove and discard bay leaves.
Serve warm topped with chopped fresh parsley.