Heat a medium (10-inch) well-seasoned cast iron or nonstick skillet on medium-high. Drizzle with 1 tablespoon of olive oil and add the spinach. Cover with a lid and cook until it is soft enough to break apart; this should take 2 to 3 minutes if it’s thawed and about 5 to 8 minutes if it’s still frozen. Remove the lid and stir to break up the spinach and cook uncovered until most of the liquid has evaporated but it’s not completely dry, 2 to 4 minutes. Stir in the garlic powder and season with ¾ teaspoon salt and about 1 teaspoon black pepper.
Reduce heat to medium. Add the cream cheese and stir well until combined. Cook for 2 minutes until the mixture is warmed through.
Make a divot for each egg and pour a little olive oil into the hole before adding the egg. (This is easiest to do one divot at a time.) Once you have added all the eggs, cover and cook for 5 to 8 minutes, until whites are just set and yolks are cooked to your liking.
To serve, drizzle with olive oil and eat immediately, with bread.