In a bowl, whisk the egg whites, sesame seeds, ¼ cup cornstarch, ½ teaspoon salt, and ¼ teaspoon pepper. Dip the chicken in batter and shake off excess.
Heat 2 tablespoons of the oil in a large nonstick skillet over medium-high heat. Add half the chicken.
Cook until golden brown and cooked through, 2 to 3 minutes per side. Transfer to a plate. Repeat with 1 tablespoon oil and remaining chicken.
In a small bowl, combine the soy sauce, ginger, sugar, 1 tablespoon water, and remaining teaspoon cornstarch.
Heat the remaining tablespoon oil in a large skillet over medium-high heat. Add the bok choy and cook, turning, until just starting to soften, 1 to 2 minutes.
Add the soy sauce mixture and jalapeño and cook until liquid has thickened slightly and bok choy is tender, 3 to 4 minutes. Serve with the chicken.