In a 10-inch heavy skillet warm 2 tablespoons of the olive oil over medium heat. Add the onion and cook, stirring frequently, until soft and translucent but not browned.
Add the kale, 1 tablespoon of the oil, and a pinch of salt, and stir until just wilted. Reduce the heat to low, cover the pan, and cook for 15 minutes, stirring occasionally.
The kale should be very tender, and the onions should have taken on a rosy brown color. Set aside.
Break the eggs into a medium bowl, and beat them well with a fork. Add the cheese and salt, and beat again to blend. Add the kale and onion mixture, and beat to mix well.
Wipe any burnt bits from the skillet, and add the remaining ½ tablespoon oil. Place the pan over low heat.
When it is warm, pour in the egg mixture. If necessary, use the fork to gently push the kale around a bit, so it is evenly distributed. Cook over low heat until the bottom of the frittata is lightly browned – tease the edge up with a heatproof spatula and peek underneath – and the top looks mostly set.
Remove the pan from the heat and slide it under the broiler until the top is nicely browned, 30-60 seconds. Don’t walk away from it while it’s under the broiler; it cooks very quickly.
Cut into wedges, and serve warm or at room temperature, with additional salt, if needed.