To begin, preheat your oven to 350°F (175°C). Lightly grease a 9 inch round or square baking pan, or line it with parchment paper. In a small saucepan, warm the milk over low heat until lukewarm, then set it aside to cool slightly. This step ensures smooth incorporation with the batter.

In a large mixing bowl, whisk the sugar and melted butter together until smooth. Add the eggs one at a time, beating well after each addition. Whisking thoroughly at this stage ensures a fluffy and even batter.

Slowly pour in the lukewarm milk, followed by the vanilla extract. Stir gently until the liquid ingredients are fully combined. Avoid overmixing to maintain the batter's light texture.

In a separate bowl, sift together the all-purpose flour, baking powder, and salt. Gradually fold the dry ingredients into the wet mixture using a spatula. Incorporate them gently to avoid deflating the batter.

Add the grated Parmesan cheese to the batter and mix until evenly distributed. This cheese is essential to the traditional flavour, offering the signature sweet savoury balance of Quesadillas Salvadoreñas.

Pour the batter into the prepared baking pan, smoothing the top with a spatula. Sprinkle a generous layer of sesame seeds over the batter for an authentic finishing touch. These seeds provide a nutty flavour and golden texture.

Bake the quesadilla in the preheated oven for 30-35 minutes, or until the top is golden brown and a toothpick inserted into the centre comes out clean. Allow it to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.

Slice the quesadilla into wedges or squares and serve at room temperature. Pair it with a cup of coffee or a glass of milk for an authentic Salvadoran experience. For presentation, place the slices on a decorative plate and garnish with a light dusting of powdered sugar if desired.