Preheat the oven to 400°F and line a baking sheet with parchment paper.
Sauté the filling: In a skillet over medium heat, add a splash of oil and sauté the shallot for 2–3 minutes until softened. Add the spinach and cook until wilted. Transfer to a bowl and let cool slightly.
Mix the filling: To the spinach mixture, add cream cheese, feta, oregano, salt, and pepper. Mix until well combined and creamy.
Prepare the phyllo: Lay one sheet of phyllo dough on a clean surface. Lightly brush with melted butter. Top with another sheet and repeat until you have 3 layers. Repeat this process for the second salmon fillet.
Assemble: Place a salmon fillet in the center of the phyllo stack. Top with half the spinach-feta mixture. Fold in all sides over the salmon until you have a parcel. Brush the tops and the sides of the parcel with butter and sprinkle with sesame seeds. Repeat with the second fillet.
Bake: Bake for 17-20 minutes, or until the phyllo is golden brown and crispy.