Submerge the figs, dates and apricots in boiling water and set aside for about 30 minutes or until the fruit is very soft.
Drain and place the fruits in a blender or food processor. Process till you have a rather smooth and thick paste. Add just enough water -- 1 or 2 tablespoon -- if needed to keep the blades moving, but don't let the mixture get liquid.
Heat the coconut oil in a heavy-bottomed saucepan.
Add the fruit paste and cook, stirring almost constantly, for 10 minutes.
Add the powdered apricots and stir in.
Add the walnuts and cook, stirring, for another 10-15 minutes until the mixture darkens and glistens.
Grease a small plate and turn the fruit and nut mixture into it.
Using your hands and a plastic wrap or a spatula flatten the mixture into a five-inch square.
Let the burfi cool completely until it sets. Then cut into diamond-shaped pieces or squares.