We decided to combine the flakiness and nutty flavors of baklava with the fruit of a strudel. If your apricots are very ripe, don't let them sit in the honey syrup too long before you assemble the strudel--they'll turn to jam. But if they're a little firm or very tart, let them macerate a bit longer to soften and absorb the sweetness.
1. Preheat oven to 375°. Bring honey and 1/4 cup sugar to a simmer in a saucepan, stirring to blend. Remove from heat and add apricots; set aside.
2. Whirl nuts, cardamom, and remaining 1/4 cup sugar in a food processor until mostly ground. Set aside 2 tbsp.
3. Lay a piece of parchment paper on a work surface. Working with 1 filo sheet at a time, set on paper, brush with some butter, and sprinkle with a scant 2 tbsp. nut mixture; repeat, stacking filo and pressing down to seal.
4. Spoon apricots with a bit of honey mixture on filo stack along a long side. Roll up. Arrange roll on a diagonal on a rimmed baking sheet lined with parchment. Brush with more honey mixture; sprinkle with reserved 2 tbsp. nut mixture.
5. Bake until browned and juices are bubbling out the ends, 15 to 20 minutes. Let cool completely before slicing.