Set your Instant Pot to the "Sauté" setting and melt the butter. Once melted, add the chopped garlic and diced onions, cooking them gently until they become fragrant—be careful not to let them brown. Next, pour in the chicken broth, stirring to deglaze the pot and lift any browned bits from the bottom. Add the sliced carrots, celery, cubed red Idaho potatoes, and the bone-in, skin-on chicken breasts, along with the dried thyme, sage, marjoram, and 1½ teaspoons of salt. Stir to combine, then secure the lid on the Instant Pot to proceed with cooking. This method builds flavor through sautéing while ensuring everything is well mixed before pressure cooking.
Switch your Instant Pot to the "Pressure Cook" setting and set it to high for 15 minutes. Ensure the valve is in the sealing position to trap steam. Once the cooking time is complete, carefully release the pressure manually. This quick cooking method allows the flavors to meld beautifully while ensuring the chicken becomes tender and the vegetables are perfectly cooked.
Carefully open the lid of the Instant Pot and transfer the chicken breast to a plate. Discard the skin and bones, then shred the chicken into bite-sized pieces. This step not only makes the chicken easier to eat but also allows it to absorb the flavors of the soup as you mix it back in.
In a small bowl, whisk together the milk and all-purpose flour until smooth. Set the Instant Pot to the "Sauté" setting and bring the soup to a gentle boil. Add the egg noodles and cook them according to the package instructions. Once the noodles are tender, stir in the milk and flour mixture to thicken the soup. After the soup reaches your desired consistency, return the shredded chicken to the pot and mix well. Taste the soup, and adjust the salt if needed to enhance the flavors, ensuring a deliciously balanced dish.
Turn off the Instant Pot and ladle the creamy chicken noodle soup into bowls. Garnish each serving with a sprinkle of black pepper and a touch of fresh parsley for a pop of color and flavor. This final touch not only enhances the presentation but also adds a bright, herbal note to the comforting dish. Enjoy your warm, homemade soup!