Place the rack in lowest position in the oven. Preheat the oven to 400°F.

Roll out the puff pastry and place it in a 9-inch tart pan with a removable bottom.

Roll a rolling pin over the tart pan to trim the puff pastry. Place parchment paper over the pastry in the bottom of the tart pan and fill with pie weights or dried beans. Partially bake for 20 minutes.

Remove the pie weights and parchment and bake for 5 to 10 minutes more until golden brown.

Remove from the oven and cool on wire rack while you prepare the filling. Maintain the oven temperature at 400°F.

Remove the stems from the spinach, place the leaves in a sink filled with water and allow the dirt to fall to the bottom. Carefully remove from the water and repeat. Drain in a colander.

Remove the tough spines and thick stems of the kale. Wash in the same manner as the spinach and drain. Steam the kale until wilted, 7 to 8 minutes. Remove to the colander to drain again.

Steam the spinach until wilted, 4 to 5 minutes. Remove to the colander to drain again.

Press on the spinach and kale to remove most of the moisture. Coarsely chop the spinach and kale and place in a large mixing bowl.

In a food processor, combine the cottage cheese, eggs, and milk. Puree until you have a smooth custard with barely noticeable pips of cottage cheese.

Pour the custard over the greens.

Stir in the currants, salt, nutmeg, and pepper. Pour the filling into the prepared pie shell. Pat and smooth the filling until compact, smooth, and flat across the top. Bake until the filling is set, about 25 minutes.

Cool for 5 minutes before serving.