CRUMB TOPPING: 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 apricots and the edge of the batter as evenly as possible. Bake the cake 1 hour until a knife inserted in the center comes out 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 cake onto the rack, remove the plate and cool.
CAKE BATTER: PREHEAT THE OVEN TO 350F. Butter a 10-inch round, 2-inch deep cake pan and line the bottom with a disk of parchment or wax paper. In a large mixer bowl, beat the butter and sugar until soft and light. 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. Rinse and halve the apricots. Remove the pits with the bowl of a small spoon if they resist. Arrange the apricot halves cut-side up 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 mound slightly in the center of the cake; the top will even out as the cake bakes.
Use this recipe with peaches, sour cherries or pineapple with equally good results.