Preheat the oven to 350 F degrees.
In a bowl, combine the cream cheese and feta, mashing and stirring with a fork until well blended. Add the scallions and spinach and combine well. Spread the mixture evenly over 1 salmon fillet. (The filling will be about 3/4-inch thick.) Top with the second salmon fillet. Brush both sides with olive oil, turning over carefully with a spatula, and place on a shallow baking pan. Bake for 20 minutes; test for doneness with a toothpick. To serve, slice carefully with a sharp, serrated knife.