Thaw phyllo dough completely in refrigerator overnight.

Preheat your oven to 350 degrees. Line a 9x13 pan with parchment paper (if desired).

Working with two sheets of phyllo dough at a time (stacked one on top of the other), hang sheets from your hands and gather/fold into a loose accordion about 1 inch thick. See this video for a demonstration.

Place in prepared pan, folds facing up, and repeat until all phyllo dough has been used. Lightly adjust/fluff your phyllo accordions as needed to make sure they fill the pan loosely with no dense folds.

Move pan to oven and bake phyllo only, for 10 minutes.

Remove from oven and drizzle the melted butter evenly over the phyllo dough. Return to oven and bake for an additional 10 minutes.

During this second bake, prepare the custard by whisking together the milk, eggs, sugar, and vanilla extract. Hint: a large measuring container or bowl with a spout is best for this step to ease pouring. Remove phyllo from the oven and pour the custard evenly over the top. Return to oven, and bake until the top is golden and crispy, about 30-40 minutes.

When the baking time is nearly up, prepare the syrup. In a small saucepan over medium heat, combine sugar, water, and lemon juice. Whisk to combine and heat to a simmer. Continue to simmer until some of the moisture has evaporated and the syrup has thickened (think the consistency of maple syrup-- if it's too thin it will result in a soggy cake).  This generally takes me about 10 minutes, but could take longer depending on the pan you're using.  Remove from heat.

When cake is golden and the 30-40 minute bake is complete, remove the pan from the oven and drizzle the warm syrup evenly over the top.

Allow cake to cool to room temperature, cut, and serve.