Roughly chop about 1/2 cup of the cranberries. Put the rest into a big bowl.
Put the chopped cranberries and cut-up figs and apricots into a small saucepan and stir in the port. Bring to a simmer and cook for about 5 minutes, until most of the port has been absorbed by the fruit. Set aside to cool.
To the big bowl with the whole cranberries, add the rest of the ingredients. Stir until combined.
When the fig-apricot mixture has cooled somewhat, add it to the whole-cranberry mixture and stir to combine.
Roll out your bottom disk of dough. Ease it into the pie pan. Trim edges.
Fill the bottom crust with the fruit filling.
Roll out the top disk of dough and lay it on top, trimming, rolling and crimping the edges.
Put the pie in the freezer to chill while the oven preheats.
Preheat the oven to 425. When it is fully up to temperature, take the pie out of the oven. Make a few decorative vents in the top-center of the pie. Brush lightly with egg white and sprinkle with sugar.
Bake at 425 for about 15 minutes.
Turn the oven down to 375. Bake for another 45 minutes or so, checking to see that the top crust is a nice deep golden color and that the juices are bubbling through the vents.
Cool to room temperature before serving.