Melt the butter in the microwave or in a saucepan.
In a bowl, mix well to combine the pumpkin, sugar, pumpkin pie spice, vanilla, cinnamon, and salt.
Preheat oven to 350 degrees F with the rack in the middle. Grease the bottom and sides of a 9"x13" baking sheet with butter. Unroll the phyllo sheets and cover with lightly dampened paper towels while you are working, the sheets dry out quickly.
Brush some melted butter onto the bottom of the pan. Lay down a sheet of phyllo. Brush butter on the sheet. Continue this 7 more times so you have 8 buttered sheets on the base.
Using a soft spatula, spread on a thin layer of the pumpkin mixture. Lay on 4 sheets of phyllo, butter in between each. Spread the pumpkin mixture over the top. Continue with the 4 buttered slices and the pumpkin until you have used up the pumpkin mixture.
Top the baklava with 8-10 more phyllo slices, buttering in between. Brush the very top with butter. With a sharp knife, slice the baklava into desired servings. Bake for 45-50 minutes.
While the baklava is baking, heat the maple syrup in a saucepan and bring to a simmer with the cinnamon & vanilla. Remove from the heat.
Remove the baklava from the oven and top with the hot maple mixture. Serve warm or at room temperature.
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