Add the chopped potatoes and smoked chicken to a large pot. Pour in the chicken stock or water and bring to a gentle simmer. Cook over low to medium heat for about 20 minutes, until the potatoes are fork-tender but still holding their shape.

While the potatoes cook, heat a little oil in a skillet over medium heat. Add the chopped onions and cook for about 4 minutes, until they begin to soften. Add the carrot and cook for another 5 to 6 minutes, stirring occasionally.

Add the butter and mushrooms to the skillet. Cook for about 5 to 7 minutes, stirring occasionally, until the mushrooms release their moisture and begin to turn lightly golden.

Add the salt, paprika, and black pepper. Stir well and cook for about 1 minute, until the spices become fragrant and coat the vegetables.

Transfer the sautéed vegetables and mushrooms to the pot with the potatoes and smoked chicken. Add the cream cheese and stir gently over low heat until it melts completely into the broth and the soup becomes smooth and creamy.

Taste and adjust the seasoning if needed. Remove from the heat, sprinkle with fresh parsley, and let the soup sit for a few minutes before serving.