Preheat oven to 350 degrees. Butter a 10-inch round cake pan, 2-inches deep and line the bottom with a disk of parchment or wax paper.
In a large mixing bowl, beat the butter and sugar until light and soft. Add the egg and continue beating until light. Add the yolks one at a time, beating well between each addition. Beat in the vanilla. Sift together the flour and baking powder and stir into the batter. Spread the batter evenly in the prepared pan.
Arrange the apricots skin side down on the batter in concentric rows, overlapping slightly, leaving a margin of about 1-inch around the edge. Don't be concerned if the apricots mounds slightly in the center of the cake, the top will even out as the cake bakes.
For the crumbs, mix the flour, sugar and cinnamon in a bowl. Melt the butter and stir it in evenly. Rub the mixture to coarse crumbs by hand. Scatter the crumbs over the apricot and the batter at the edges as evenly as possible. Bake the cake 1 hour until a knife point inserted in the center emerges clean. Cool the cake in the pan for about 15 minutes and invert a plate on it. Invert onto the plate and lift off the pan. Peel off the paper and invert a rack on the cake. Invert onto the rack and cool.
Variations: Substitute 8 pitted and quartered plums or 3 cups fresh cut pineapple.