Preheat the oven to 350 degrees F. Equipment: I used a 9 x 12-inch baking dish. You can also use a quarter baking sheet. I've even used a 9-inch round cake pan and it turned out beautifully. You may have to trim your phyllo dough to fit the sheets. I had to do this with my casserole dish, so just a heads up on that.
In a medium bowl, mix together the pumpkin puree, sugar, brown sugar, cinnamon, salt, nutmeg, cloves, cardamom and egg.
Next, grab a clean kitchen towel and dampen it, being sure to wring out any excess water. Place it over the thawed phyllo dough as you assemble the baklava. (Phyllo dough tends to dry out very quickly and assembling the baklava takes a bit of time. The damp kitchen towel will help with this.)
Brush the first sheet of phyllo dough with melted butter and transfer it, buttered-side down, into the baking dish. Repeat this process for the next 7 layers. Top the 8th layer with a few teaspoons of pumpkin mixture, spreading it out evenly. Sprinkle the pumpkin with a small handful of chopped walnuts. (Eight bottom layers of phyllo will give you a sturdy piece of baklava, versus a flimsy one.)
Butter the next 5 sheets, placing them buttered-side down into the baking dish. Top the 5th layer of phyllo dough with a few teaspoons of pumpkin mixture and walnuts. Repeat this for the next two layers. You should end up with four layers of baklava. Using a sharp knife, slice the baklava into 1-inch diamonds or squares. Transfer to the oven to bake for 15-20 minutes, until the top is lightly golden brown and crisp.
While the baklava is baking, let's make the topping! In a small skillet, mix together the honey, brown sugar, cinnamon and salt. Heat until the sugar is dissolved. When the baklava comes out of the oven, drizzle the honey mixture on top. Allow it to sit for 1-3 hours so it has a chance to marinate!