Simmer apricots, water, sugar and brandy in large saucepan for about 10 minutes. Drain, reserving about 1/4 cup of cooking liquid. Take 4 tablespoons of the reconstituted apricots and purée with poaching liquid in a food processor.
Melt brown sugar and butter together in saucepan until hot and bubbling. Add apricot purée and cook together, about 30 seconds. Immediately spread mixture on bottom of 9-inch cake pan well coated with nonstick cooking spray. Arrange remaining apricots in concentric circles atop mixture.
Sift together cake flour, sugar, cocoa powder, salt and baking soda.
In mixing bowl, beat together mayonnaise, coffee and vanilla until thoroughly blended. Gradually add dry ingredients and beat until smooth.
Pour batter over caramel and apricots in cake pan and bake for about 30 minutes in 350 degree F oven, or until inserted wooden pick comes out clean. Let cool for 5 minutes, cover with cake plate and invert. Let cool for 15 minutes more. Serve with fresh whipped cream.