Place mushrooms, carrots and onion in a 4-quart slow cooker and add broth. Rub turkey with oil, sage, thyme, salt and pepper and place on top.
Cover and cook on high for 2 to 3 hours until the thickest part of each tenderloin reaches 165°F and carrots are tender; begin checking turkey after 2 hours.
During the final hour, bring barley and 3 cups water to a boil in a saucepan, cover and simmer on low for 50 to 60 minutes until chewy-tender, then drain excess water.
Lift turkey to a plate and rest for 10 minutes. Pour the vegetables and cooking broth into a saucepan and bring to a simmer.
Stir cornstarch with 2 tablespoons cold water and whisk into the broth. Simmer for 2 to 3 minutes until lightly thickened.
Slice turkey across the grain and divide it with barley and vegetable gravy among 4 plates.