Cut the onion, carrots, and celery into 1/4-inch dice. Set aside in a medium bowl. Slice the mushrooms, finely chop the thyme and rosemary, and set them aside in another bowl.

Heat the oil in a Dutch oven over medium-high heat. Add the chicken and sprinkle with the salt and pepper. Cook until meat is golden on the underside and releases easily from the pan, 4-7 minutes. Flip with tongs and cook until golden on second side, 2-4 minutes (it's OK if the chicken isn't completely cooked through). Transfer to a cutting board, and set aside.

Add the oil, onion, carrot, celery, salt, and pepper to the Dutch oven and cook over medium-high heat, stirring occasionally, until vegetables are tender and beginning to brown, 6-9 minutes. Add the garlic and cook until fragrant, about 30 seconds.

Stir the mushrooms, herbs, and wine into the vegetable mixture. Cover and cook to until mushrooms soften and release their liquid, 5-7 minutes. Remove lid and cook, stirring occasionally, until liquid evaporates and mushrooms begin to brown, 4-5 minutes.

Add the flour and cook until lightly toasted and fragrant, 1-2 minutes. Whisk in the chicken broth.

Whisk in the cream cheese. Slowly whisk in the remaining broth. Chop the chicken into 1/2-inch pieces, and stir into the soup.

Bring the soup to a boil, then reduce to a simmer and cook until slightly thicker, 5-7 minutes. Meanwhile, chop the parsley and stir half into the soup.

Season soup to taste with salt. Ladle into bowls, sprinkle with remaining chopped parsley, and add a parsley sprig to each serving.