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

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

Lay 1 sheet puff pastry on a lightly floured surface; cut in half lengthwise. Roll out one half with a rolling pin until wide enough to fold twice lengthwise. Combine egg and milk in a small bowl.

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

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

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