For the pastry:
Thaw phyllo dough according to package directions. Heat oven to 350°F and arrange rack in the middle.
Place almonds in a food processor with half of the sugar, and pulse until they are minced, about 15 to 20 pulses. (You want the nuts in fine, even pieces, but don’t process them to a meal.) Transfer to a medium mixing bowl. Repeat the process with walnuts and remaining sugar. Add minced walnuts, salt, crushed fennel seeds, and ground cinnamon to almond mixture. Toss until evenly combined.
To assemble baklava, brush bottom and sides of an 8-by-8-inch baking dish with some of the melted butter.
Remove thawed phyllo from the box and cover it with a damp towel (to prevent phyllo from drying out and cracking during assembly). Cut 20 sheets of phyllo in half. Set one half aside, covered with the damp towel. Cut the other half into 7-by-7-inch squares (dough should fit inside the 8-by-8-inch baking dish). Repeat with the other half, keeping extra sheets covered as you work.
Lay one phyllo square in the bottom of the prepared baking dish. Using a pastry brush, generously brush the sheet with melted butter. Repeat with 19 squares of dough, to create a 20-sheet-thick layer.
Evenly distribute nut filling over the phyllo stack, and drizzle with 4 tablespoons of the melted butter. Cover filling with another layer of phyllo dough and brush with melted butter. Continue layering remaining 19 squares of phyllo, brushing each with more butter.
Slice entire dish of baklava on the diagonal, 5 times in one direction and 5 times in the opposite direction, to create about 26 “diamonds.” Pierce one whole clove into the center of each pastry diamond, and place the baking dish in the heated oven. Bake pastry until top is golden brown and crisp, 50 to 60 minutes (edges will be dark but should not burn). Meanwhile, make the syrup.
For the syrup and assembly:
In a medium saucepan, combine sugar, water, honey, cinnamon stick, vanilla bean and seeds, lemon, and cloves. Bring to a boil over high heat, then reduce heat to medium low and simmer, stirring occasionally, until sugar is dissolved and mixture is slightly thickened, about 10 minutes. Strain into a small bowl to cool.
When baklava is finished, remove from the oven and place on a cooling rack. Pour warm honey syrup over the top of the baklava. Let cool to room temperature, at least 6 hours or overnight, to allow pastry to absorb syrup.
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