Bring medium pot of water to a boil. Reserve 4 thick spears asparagus, then cut others into 2-inch pieces. Add 1 teaspoon salt to water, then add asparagus pieces and cook until bright green, about 2 minutes; immediately transfer to bowl of ice water to cool. Drain and pat dry. Season chicken with ½ teaspoon each salt and pepper. Heat 1 tablespoon olive oil in a large skillet on medium-high, add chicken and cook, tossing occasionally, until golden brown on all sides and just cooked through, about 12 minutes. Into a large bowl, grate zest from lemon and squeeze in juice. Whisk in mustard and remaining tablespoon oil, then stir in pecorino. With vegetable peeler, pressing down firmly, create long strips from reserved asparagus. Add to bowl of dressing along with cooked asparagus and toss to coat; fold in chicken, mixed greens and almonds.