Heat oil in a skillet over medium heat and cook garlic until fragrant, 1 to 2 minutes. Stir in spinach and cook until warmed through, 3 to 5 minutes; season with salt and mix well. Transfer to a bowl and mix in feta cheese.

Preheat oven to 400 degrees F (200 degrees C). Grease 2 baking sheets.

Lay 1 sheet of puff pastry on a lightly floured surface and cut in half lengthwise. Roll 1 half out with a rolling pin so it is wide enough to fold twice lengthwise. Mix egg and milk together in a small bowl.

Spread 1/6 of the spinach mixture lengthwise in the center of the puff pastry. Roll one side over the filling and brush the other side with egg-milk mixture. Roll over again to seal.

Brush top of roll with egg-milk mixture and sprinkle with sesame seeds. Cut roll into 6 small rolls. Repeat with the remaining puff pastry. Place cut rolls onto the prepared baking sheets.

Bake in the preheated oven until spinach rolls are puffed up and golden, 20 to 25 minutes.