Heat 1 tablespoon of olive oil in a large nonstick skillet over medium-high heat. Add the garlic, and saute for a minute or so until fragrant. Add the kale, stirring constantly. Cook for for 2 to 3 minutes or until just wilted. Season with salt and pepper. Divide onto two plates.
Wipe out the skillet and add the remaining tablespoon of oil to the pan. Heat the oil for a minute or so and crack the two eggs into the pan. Reduce the heat to medium and let cook for a couple of minutes until the whites begin to harden. Add a few tablespoonfuls of water to the pan, so the eggs begin to steam a bit. Continue to cook until the yolks just begin to set. (If you want the egg yolks firmer, cook longer.)
Place one egg on top of each pile of greens; serve immediately!