Prick potatoes and bake in middle of oven for at least 1 hour, or until very soft. Allow to cool and then scoop flesh into a bowl.
In a saucepan cover apricots by 1 inch with cold water and simmer until soft, about 30 minutes. Reserve 2 tablespoons of the cooking liquid and drain apricots.
Puree apricots in a food processor with the granulated sugar and reserved liquid, until smooth.
Add puree and salt to potatoes. Beat with an electric mixer until smooth. Spread mixture into a greased shallow 2-qt baking dish. (Note: Puree may be prepared up to this point 1 day ahead and kept chilled and covered).
Reduce oven temperature to 400.
In a small bowl blend remaining ingredients (flour, brown sugar, butter, pecans, and dash salt) with your fingers until combined well. Sprinkle over puree. Bake in oven until heated through and topping is bubbly, about 15 minutes.