Heat the olive oil in a medium ovenproof nonstick skillet over medium-high heat. Add the onion, garlic, and ¼ teaspoon each salt and pepper and cook 8 to 10 minutes, stirring occasionally.
Add as much kale to the skillet as will fit. Cook until tender, 5 to 7 minutes, adding more kale when there’s room. Remove from heat.
Stir in the eggs, beaten, and the Etorki. Transfer the skillet to oven.
Bake until almost set, 6 to 8 minutes.
Switch oven to broil and broil until golden brown and set, 1 to 2 minutes.