Preparation:

Using a sharp serrated knife, thinly slice off two of the ends of the cake (save for another use); you should now have what resembles a loaf.  Slice the cake into 8 even slices, about 1/3 inch thick.  Lay on a clean work surface. Spread mascarpone on one side of 4 pieces, and apricot jam on the other 4, fold together to form a "sandwich".  In a large shallow bowl, beat the eggs, add the cream and a pinch of salt and mix until well combined.  Heat the oil in a large skillet or griddle over medium heat; when hot, dip each "sandwich" on both sides in the egg mixture and then put onto the hot griddle (do not dip the sandwich until ready to cook them, do in batches if necessary); cook until browned, then carefully turn and cook the other side.  Serve whole, or cut in half, sprinkled with powdered sugar, if desired.
*Cook's Note: While I think mascarpone is the best choice, you could substitute softened cream cheese if desired.
Variation: Use either orange marmalade or peach jam in place of the apricot jam.