Preheat oven to 375ºF. Preheat a heavy skillet to med-high heat.
Add the chopped sun-dried tomatoes and chopped broccolini to the pan. Add the water and stir to coat. Lower the heat to medium and continue to cook for 1 minute before removing from heat.
In a large bowl, combine the eggs, coconut milk, salt, black pepper, and chives. Add the cooked veggies to the egg mixture and stir to combine.
Grease a muffin pan with unrefined coconut oil and pour the mixture into each cup 3/4 of the way full, so you have 10-12 total filled.
Bake in the preheated oven for 15 minutes or until the eggs are just set. Remove and let cool. Serve warm or store in the fridge, covered, for up to 4 days.