Prepare Lemon-Shallot Dressing by combining shallots, lemon juice, ⅓ cup olive oil, and ¼ tsp. each salt and black pepper in a glass jar or small mixing bowl; mix to combine. Set aside.
Heat remaining 2 tsp. olive oil in a large skillet over medium heat. Once hot, add asparagus and sauté for 5 minutes, tossing occasionally, until crisp-tender. Season with remaining ¼ tsp. salt, and transfer to a bowl. Let sit for 5 minutes.
To the bowl with asparagus, add pistachios, dill, parsley, and feta. Season with remaining ¼ tsp. black pepper. Pour dressing overtop, and toss to combine.
