Heat 2 tablespoons olive oil in large, deep skillet over medium heat. Add mushrooms, ½ teaspoon salt and several grinds of black pepper; stir to coat. Stirring occasionally, cook 5–7 minutes, or until soft and browned. Remove from pan, set aside. Work in batches if necessary.
Wipe out pan and return to heat. Add remaining 2 tablespoons olive oil, onion, shallot and remaining ¼ teaspoon sea salt. Cook, stirring periodically, 5–8 minutes, or until softened.
Add garlic, thyme and rice; stir. Simmer 1 minute; add wine. Continue simmering 1–3 minutes, or until wine cooks down.
Add stock ¾ cup at a time, stirring constantly, and allowing each addition to be absorbed before adding the next. With final stock addition, stir in 2/3 of sautéed mushrooms. Cook until risotto is creamy and rice has a slight al dente bite. Add lemon zest if using. Stir in cheese, season to taste.
Top with remaining sautéed mushrooms, garnish with chives and serve with more grated cheese, if desired.
