Bring water to a boil in a saucepan; stir in oats and salt. Reduce heat to low and cook oats until tender and water is absorbed, 25 to 30 minutes.
Chop kale into 1/4-inch pieces. Heat 1 tablespoon olive oil in a skillet over medium heat. Add kale; cook and stir until softened and bright green, about 5 minutes. Reduce heat to low and cover skillet. Cook until kale is tender, 3 to 4 minutes more. Transfer kale to a plate.
Return skillet to medium heat, add remaining oil. Crack egg into the skillet and cook until egg is white on the bottom layer and firm enough to flip, 2 to 3 minutes. Flip egg gently to avoid cracking yolk. Cook egg to desired doneness, 1 to 3 minutes more.
Pour oatmeal into serving bowl. Top with kale and egg; season with harissa, salt, and pepper.