Dissolve 2 tablespoons salt in 6 cups cold water in Dutch oven. Submerge chicken in water. Heat pot over medium heat until water registers 170 degrees. Turn off heat, cover pot, and let sit until chicken registers 165 degrees, 15 to 17 minutes. Transfer chicken to paper towel–lined plate and refrigerate until cool, about 30 minutes. Transfer chicken to cutting board, pat dry with paper towels, and shred into bite-size pieces.
Process mayonnaise, sour cream, herbs, water, lemon juice, and garlic in blender until smooth, scraping down sides of blender jar as needed. Stir in chives and season with salt and pepper to taste; set aside.
Heat oil in 10-inch nonstick skillet over medium-high heat until shimmering. Add asparagus, pepper, and pinch salt and cook, stirring frequently, until crisp-tender, 5 to 7 minutes; transfer to bowl.
Toss spinach with half of dressing and divide among individual serving bowls. Top evenly with chicken, asparagus, and avocado. Drizzle with remaining dressing and sprinkle with pistachios. Serve.