Heat 1/2-inch of oil in another large heavy skillet over medium heat until it registers 350° F on thermometer.
While oil heats, beat egg whites with 1/2 teaspoon salt, using an electric mixer until they just hold stiff peaks.
Whisk in the yolks, two at a time, just until incorporated. Next, whisk in 1/4 cup flour.
Spread 1 cup of flour onto a plate. Generously dust chilies with the flour, coating all sides. Gently shake off excess flour.