Butter and flour 2 8" round cake pans or use silicone.
In mixer, combine eggs, sugar and vanilla. Mix well.
Stir over boiling water or the burner for about 30 seconds so the mix is barely lukewarm. Remove from heat. Beat on medium to high 10 minutes. The mixture should make a thick, pale yellow ribbon and have at least tripled in volume.
Sift in flour with one hand and fold mixture with the other using a wide spatula.
Add butter, pouring and folding the same way.
Fill pans about 3/4 full. Place pans on a cookie sheet and bake for 22-25 minutes.
Remove from oven and after 5 minutes turn upside down on racks. Bottoms and sides should be pale golden. The cakes should be flat (no sagging) and soft and springy to the touch. When cool, place in plastic bags to keep fro drying. The will keep for a few days without refrigeration.
In heavy saucepan melt the appricot jam slowly over low heat to avoid scorching. When liquefied, strain through a metal sieve and reserve.
Mix ingredients together and reserve.
Coffee Butter Cream:
In a saucepan combine sugar and coffee. Bring to a boil and boil for 3 minutes. Set aside.
In mixer bowl at medium beat yolks adding sugar syrup slowly. Then beat at high speed until the mixture is the consistency of light mayonnaise, about 5-6 minutes.
Return to medium speed and add butter piece by piece, until smooth. Butter cream should not be refrigerated before frosting the cake.
Using a long bladed serrated knife, cut each cake layer into three horizontal slices. Keep on hand flat on the cake and hold the knife perfectly flat so that slices are the same thickness. This requires some practice.
Place a top or bottom layer crusty side down on th ecake plat and moisten with some rum syrup. Spread 1/4" layer of butter cream all over with a thin flexible metal spatula. Place another layer on top. Moisten with more rum syrup and spread 3 tablespoons melted apricot jam on top. Continue alternating fillings and finish with butter cream (be sure to reserve some for decorating). Spread cream evenly and smoothly on the sides. Using a serrated edge, hold the knife on an angle and slide left to right in a swivel motion to decorate the top.
Place reserved butter cream in pastry bag fitted with a fluted tube and decorate top and bottom edge.
Refrigerate until ready to serve. Do not cut wedges too thick.