1. Heat 1 tablespoon oil in a large skillet over medium-high heat. Cook half the mushrooms with 1/2 teaspoon salt, stirring occasionally, until deep golden, about 5 minutes, and transfer to a bowl. Repeat with 1 tablespoon oil, remaining mushrooms, and 1/2 teaspoon salt. Cook shallot in 1 tablespoon oil over low heat until softened. Add 2 tablespoons vinegar and simmer until reduced by half.

2. Remove from heat; whisk in creme fraiche and remaining tablespoon vinegar. Whisk in remaining 5 tablespoons oil until combined. Add chives and thyme, and season with salt and pepper; let cool. Combine lettuce, barley, mushrooms, nuts, and parsley. Add dressing, tossing to coat. Season with salt and pepper.