Preheat the oven to 375ºF. Line two large baking sheets with parchment paper. Unroll the puff pastry sheets on the work surface and cut into 16-20 identical squares. Gently brush all the edges of the squares with beaten egg. Place a slice of tomato and a spoonful of grated cheese in the center of each pastry square. Season with sea salt, black pepper, and dried basil.
Bring the corners of the dough together over the filling to enclose it. Set on baking sheets. Brush the pastries with the remaining egg and sprinkle generously with sesame seeds.
Place in the oven and bake for 15-18 minutes, until the puff pastry is golden, and the cheese is melted. Remove from the oven, sprinkle with fresh oregano leaves, and let cool for 10 minutes before serving.