In a medium bowl, mix together dates, apricots, ginger, rum, and sugar. Set aside and allow to soak.
Combine flour and powdered sugar in a large bowl. Add the diced butter and rub it in with your fingers until the mixture resembled breadcrumbs. Set aside.
In a small bowl, mix the eggs, lemon juice, and water. Make a well in the center of the flour mixture and pour the egg mixture in.
Work the liquid into the flour and bring the pastry together. Gently knead into a ball. Wrap in baking paper and let rest in the fridge for 15 minutes.
Heat the oven to 350 degrees Fahrenheit.
Cut the dough into two pieces (divided 1/3and 2/3rds) Roll out the larger piece of dough on a lightly floured surface. Use this dough to line the pie dish leaving the excess hanging over the sides.
Spread the filling in the pastry case and dot with the softened butter.
Roll out the remaining pastry and cut into 14 long, thin strips. Create a 7 by 7 stripe lattice.
Dampen the rim of the pastry with water before placing the lattice onto the tart. Press the ends of the lattice into the pastry rim to secure it. Crimp the edges with a fork.
Brush all visible pastry with the beaten egg.
Bake for 15 minutes, the reduce the heat to 315 degrees Fahrenheit and back for another 20 minutes or until the pastry is golden brown.
To make rum butter, beat together the butter and sugar and smooth and creamy. Gradually beat in the run.
Serve the tart with a spoonful of rum butter for each serving. Enjoy!!