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Arrange an oven rack to the middle position and heat to 350 F. Grease the bottom of a 9-by-13-inch baking dish with butter.
On a clean work surface, unroll the phyllo sheets and place them in a stack. Gather two sheets at a time and pinch them with your fingers like a paper fan or accordian, then place in the baking dish, starting with the shorter side. Repeat with the remaining phyllo sheets. Bake for 10 minutes. Remove from the oven and evenly pour melted butter on top. Return to the oven and bake for another 10 minutes.
Meanwhile, make the custard: In a medium bowl, whisk together the milk, eggs, sugar, vanilla, and lemon zest.
Remove the phyllo sheets from the oven and pour the custard evenly on top. Return to the oven and bake for about 35 minutes until the cake is golden brown, puffed and crispy.
While the cake is baking, make the lemon syrup. In a small pot, combine the honey, sugar, lemon juice, lemon zest, and water. Bring to a boil, stirring occasionally and scraping down the sides of the pot. Reduce heat to medium-low and simmer, stirring occasionally, until slightly thickened, about 5 minutes. Set aside, uncovered.
Immediately after the cake has finished baking, pour the lemon syrup evenly over the top. Sprinkle with the pistachios. Cool completely at room temperature, then slice into squares.