Preheat oven to 375°F. In a large bowl, whisk the first 6 ingredients (through oregano).
Lightly coat an 8-inch ovenproof cast-iron or nonstick 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.
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