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.
Whirl nuts, cardamom, and remaining 1/4 cup sugar in a food processor until mostly ground. Set aside 2 tbsp.
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.
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.
Bake until browned and juices are bubbling out the ends, 15 to 20 minutes. Let cool completely before slicing.