1 (1-pound) pork tenderloin, trimmed
3/4 teaspoon kosher salt, divided
1/2 teaspoon freshly ground black pepper
2 tablespoons olive oil, divided
1 (8-ounce) package button mushrooms, thinly sliced
3 garlic cloves, minced
2 tablespoons white wine vinegar
1 cup fat-free, lower-sodium chicken broth
1/4 cup creme fraiche or sour cream
2 teaspoons Dijon mustard
3 tablespoons chopped fresh flat-leaf parsley