Bring a pot of water to boil. Transfer the spinach to the boiling water and cook for 1 minute. Drain the spinach and rinse under cold running water. Thoroughly squeeze out any excess liquid and roughly chop.
Line each phyllo cup with spinach and smoked salmon pieces. Add crumbled goat cheese and a sprinkle of dill.
Whisk together the egg, heavy cream, salt and garlic powder in a small bowl.
Pour the egg mixture over the phyllo cups. Each cup should be just barely full.
Cook the salmon tartlets for 12 minutes. Allow to cool for 10 minutes before serving.