To rehydrate the apricots: Cut apricots in quarters and place in a bowl. Pour very hot water over the apricots to cover, plus about an inch of water. Let stand for 1 hour. Put apricots and soak water in a food processor and process until smooth. Measure out 1 cup plus 2 tablespoons (9 oz.) for the recipe.

Preheat oven to 350 degrees. In large mixing bowl at low speed, beat the eggs and sugar until blended. Add oil alternately with flour, mixing well after each addition. Add apricots, vanilla and rum flavoring; beat at medium speed for 2 minutes. In separate bowl, stir together topping ingredients. Pour ½ batter into greased and floured 10-inch tube pan. Sprinkle with ½ topping mix. Repeat with remaining batter and topping. Bake at 350 degrees for 1 hour 10 minutes. Cool in pan for about 5-10 minutes.

While cake is cooling in pan, heat glaze ingredients in a small saucepan on medium heat. Turn cake onto plate, with streusel topping facing up. Pour glaze over hot cake.