Warm 1 tablespoon olive oil in a medium Dutch oven set over medium heat.
Add the 2 pounds of cubed pork tenderloin in batches. Cook until the pieces are browned and no longer pink on the exterior.
Transfer the cooked pork from the Dutch oven and keep it warm while preparing the remaining components.
Place the chopped medium onion into the same Dutch oven. Cook over medium heat for approximately 3 minutes, or until the onion reaches a crisp-tender consistency.
Stir in the minced garlic clove and continue cooking for 1 additional minute, stirring frequently so the garlic does not burn.
Pour in the 4 cups of reduced-sodium chicken broth, then add the 2 pounds diced red potatoes, 1 cup sliced carrots, 1 cup sliced celery, and 8 ounces sliced fresh mushrooms.
Mix in the 2 tablespoons cider vinegar, 2 teaspoons sugar, 1½ teaspoons dried tarragon, and 1 teaspoon salt.
Bring the contents of the Dutch oven to a boil. Lower the heat, cover the pot, and simmer for 25–30 minutes, or until the vegetables are tender.
In a small bowl, whisk together the 2 tablespoons all-purpose flour and ½ cup fat-free milk until completely smooth.
Slowly pour the flour-and-milk mixture into the simmering vegetables while stirring continuously.
Return the stew to a gentle boil and cook for approximately 2 minutes, stirring throughout, until the broth has thickened.
Return the reserved browned pork to the Dutch oven and continue heating until the meat is thoroughly warmed.
Lower the heat and gently blend in the ½ cup sour cream.
Once the sour cream has been incorporated, keep the stew below a boil to help prevent the creamy mixture from curdling.
Serve the pork tenderloin stew hot. Finish each portion with chopped fresh parsley and freshly cracked black pepper, if desired.