Preheat oven to 300 degrees.
In a small bowl, add 2 cups hot water and steep currents for 10 minutes. Drain and pour rum over. Allow to steep for several hours or overnight and cool.
In a mixing bowl, add butter and use a hand held blender and blend until creamy. Add brown sugar and cream until light and fluffy. Add egg and mix until well blended. Add golden syrup, vanilla and salt and mix well. Add currants and mix by hand.
Pie Dough:
In a mixing bowl, add flour and pour oil and water over. Mix until ball forms.
In a tartlet pan, add 1-inch (approx.) ball of dough (or use a 1-inch cookie scoop) and push the dough up the sides of each tartlet. Add filling to each tartlet until about 2/3 full. Place in oven and bake for 30 minutes. Remove and allow to cool.