In a large soup pot, heat the oil over medium heat until hot. Add the roast and cook for 4 to 6 minutes, browning on all sides; remove the roast from the pot and season with the salt and pepper.
Add the mushrooms, onion, and garlic to the pot. Saute' for 5 to 7 minutes, until the onion is lightly browned. Add the broth, tarragon, and bay leaf then return the roast to the pot and bring to a boil.
Reduce the heat to low, cover tightly, and simmer for 1-1/2 hours. Stir in the barley, cover, and cook for 10 to 12 minutes.
Remove the roast from the pot, and keep warm. Remove and discard the bay leaf then add the peas and sour cream to the barley mixture, stirring constantly over low heat just until heated through. Carve the roast and serve with the barley mixture.