Heat the oven to 375°F. Thaw the spinach and squeeze it very dry in a clean kitchen towel; drain the artichoke hearts well and chop them.
In a large bowl, stir the Greek yogurt, softened cream cheese, garlic, onion powder, salt, black pepper and red pepper flakes (if using) until smooth.
Fold in the spinach, artichokes, 1/2 cup of the mozzarella and 1/4 cup of the Parmesan until evenly combined.
Spread the dip into a 1-quart baking dish and sprinkle the remaining mozzarella and Parmesan over the top.
Bake 20–25 minutes, until hot and bubbly around the edges. For a golden top, broil 1–2 minutes, watching closely.
Rest 5 minutes, then serve warm with cucumber and carrot sticks, pita chips or toasted baguette slices.