Place an oven rack in the center of the oven and preheat to 375 degrees F.
In the bowl of a food processor, pulse together the apricots, walnuts, honey, 1 tablespoon orange zest, orange juice, and cardamom, until the apricots are in 1/4-inch pieces.
Place a sheet of phyllo dough on a work surface. Brush the dough with melted butter. Place another sheet of dough on top and brush with melted butter. Repeat with remaining dough and melted butter. Using a sharp knife, trim the pastry into a 12 by 9-inch rectangle. Cut the dough into 12 (3-inch) square pieces. Gently press each piece of dough into the muffin pan. Spoon the apricot filling into the cups. Bake for 12 to 14 minutes until the pastry is golden. Remove from the oven and let the phyllo cups cool for 10 minutes. Using a dessert spoon or a small spatula, remove the phyllo cups from the pan. Place on a rack and cool completely.
Arrange the phyllo cups on a platter, garnish with orange zest, if using, and serve. Or, store in an airtight plastic container for up to 4 days.