Preheat the oven to 400˚ F. Finely crumble the goat cheese with a fork in a medium bowl, then stir in the ricotta. Brush a 12-cup muffin pan with 1 tablespoon of the melted butter; set aside 1 tablespoon melted butter in a small bowl for step 3.
Use the remaining 6 tablespoons butter for the phyllo sheets: Brush the top of a phyllo sheet all over with butter, then stack 3 more sheets on top, brushing each with butter. Cut the stack in half lengthwise, then crosswise into thirds to make 6 squares. Press each square into a muffin cup. Repeat with the remaining 4 phyllo sheets and melted butter.
Divide the cheese mixture among the phyllo-lined muffin cups, pressing with a spoon to flatten the filling into the cups. Fold in the phyllo to cover the filling, leaving a little hole in the center to vent steam. Brush the tops of the dough with the reserved 1 tablespoon melted butter. Put the pan on the oven floor and bake until the phyllo purses are dark golden brown on the bottom, 5 to 8 minutes. Reduce the oven temperature to 375˚ F; move the muffin pan to the middle oven rack and continue baking until the phyllo is golden brown and crisp on top, 30 to 40 minutes.
Meanwhile, combine the sugar, water, cardamom and orange zest in a small saucepan. Bring to a boil, reduce to a simmer and cook, occasionally pressing on the cardamom pods with a spoon, until syrupy, about 8 minutes. Strain through a fine-mesh sieve into a liquid measuring cup. Stir in the orange juice.
Remove the phyllo purses to a platter as soon as they come out of the oven. Spoon about half of the syrup on top. Let sit for a few minutes to soak in the syrup, then top with the pistachios. Drizzle with more syrup and serve warm.