Turn the pizza dough out onto a work surface; cut off and reserve one-quarter of the dough, then halve the remaining dough. Press one half evenly into a greased 9- to 10-inch cast-iron skillet.
In a medium bowl, whisk together the brown sugar, 1 teaspoon cinnamon and 1/4 teaspoon salt; toss with the pecans and currants. Sprinkle half of the nut mixture on the dough in the pan, leaving a 1/2-inch border; dot with 1 1/2 tablespoons butter. Shape the smaller piece of reserved dough into a 9- to 10-inch round and place on top of the filling. Sprinkle with the remaining nut mixture and dot with another 1 1/2 tablespoons butter. Shape the remaining dough into a 10-inch round and place on top, pressing around the edge to seal the layers. Cover with a kitchen towel and let stand until doubled in size, about 25 minutes.
Preheat the oven to 400 degrees . Melt the remaining 1 tablespoon butter and brush over the top crust. In a small bowl, combine the granulated sugar and the remaining 1/4 teaspoon cinnamon; sprinkle on top. Cut a few vents in the top crust and bake until golden, about 25 minutes. Let cool in the pan for 30 minutes.
Stir together the confectioners' sugar, milk, orange juice and a pinch of salt, then drizzle on top.