Combine the apricots, brown sugar, flour, and water I na saucepan. Cook just until the apricots have softened and the mixture is thickened. Add the vanilla and rum. Set aside.

For the crust, combine the flour, brown sugar, and baking soda in a medium bowl. Toss with the melted butter by hand until well combined. Blend in the oatmeal. Press half of the mixture into the bottom of a 9x12-inch baking dish. If time permits, refrigerate the pressed-out dough for 30 minutes. This will make the next step easier.

Carefully spread the apricot mixture evenly over the crust. Sprinkle remaining mixture over the apricots.