Heat the oil and butter in a large Dutch oven or similar deep, heavy-bottomed pot over medium-high heat. Once the butter melts, add the mushrooms and cook for 8 minutes, until mushrooms are beginning to brown, stirring occasionally.

Add the celery, garlic powder, salt, thyme, sage, and pepper. Continue cooking until the mushrooms have browned more deeply and the celery begins to soften, about 3 minutes more.

Sprinkle the flour over the top and cook 1 minute, stirring so that the flour turns golden and all of the white bits disappear. While stirring, slowly splash in the milk. Gradually add the broth, continuing to stir to prevent lumps from forming.

Add the potatoes. Increase the heat to bring the soup a low simmer, partially cover the pot, and let cook 10 minutes, adjusting the heat as needed to maintain a gentle simmer.

Stir in the frozen mixed vegetables, then partially cover once more. Continue to simmer until the vegetables are hot, the potatoes are tender, and the soup has thickened, 10 to 15 additional minutes. Adjust the heat as needed to that the stew simmers but does not bubble aggressively.

Stir in the chicken. Taste and adjust seasoning as desired. Serve hot with a sprinkle of fresh parsley.