Preheat oven to 375°F. In a large bowl, whisk the first 6 ingredients (through oregano).

Lightly coat an 8 inch ovenproof cast-iron skillet with cooking spray. Heat over medium. Add the kale and tomatoes. Cook, stirring, until hot (about 3 minutes). Add the eggs and swirl to distribute.

Transfer to the oven and bake until set and hot (about 20 minutes). Cut in wedges.