Preheat oven to 350°F. Coat a 9-inch pie plate with cooking spray. Boil 4 cups of water in a medium saucepan.
Heat oil in a medium skillet over medium-high heat. Cook onion until softened, stirring occasionally, about 5 minutes. Add artichoke hearts and tarragon. Cook until artichokes are heated through, about 2 minutes.
Meanwhile, whisk together milk, eggs, egg whites, 1/2 cup of cheese, lemon zest, salt and pepper. Pour into prepared pie plate. Scatter onion mixture evenly over egg mixture. Sprinkle with remaining 1/4 cup of cheese.
To bake quiche, create a water bath: Set a large sheet pan with sides on a flat surface. Place pie plate on sheet pan. Pour hot water around pie plate so it goes 1/2 inch up sides of pie plate (do not get water on quiche). Carefully lift sheet pan to prevent splattering water and place in oven. Bake in water bath until quiche is set in center, about 45 minutes.
To remove pie plate from water bath, slide 2 large spatulas under pie plate and remove pie plate from oven (make sure to wear oven mitts). Leave sheet pan in oven so water can cool before removing pan from oven.
Turn oven to broil. Broil quiche 3 inches from heat until golden brown, about 2 minutes. Cool 5 minutes before cutting into 8 pieces.