German Tree Cake (Baumtorte/Baumkuchen)

Ingredients

• 1 1/2 cups almond paste, tightly packed (12 oz)
• 6 tbsp half &; half
• 1 1/2 sticks butter (12 tbsp), softened
• 1 cup sugar
• 10 eggs, separated (put the whites in a bowl big enough to whip them up to stiff peaks)
• 1 1/2 tsp vanilla extract
• 1 cup cake flour
• 3/4 cup cornstarch
• 10 0z jar apricot jam
• 1 cup slivered almonds, coarsely chopped.
• 3 tbsp butter
• 1 tbsp rum, preferably dark
• 1 1/2 tsp vanilla extract
• 1 tbsp light corn syrup
• 3 oz semi-sweet chocolate chips