Step 1Place the butter, 1/2 cup of the sugar, the salt, egg yolks, lemon zest and lemon juice in the bowl of a food processor. Blend until smooth.
Step 2Place the flour and baking powder in a small bowl and mix with your fingers. Slowly add the dry ingredients to the other mixture, pulsing each time, just until the ingredients are incorporated. Refrigerate the dough until firm, about an hour.
Step 3Heat the oven to 350 degrees. Grease a 9-inch springform pan or pie pan with a removable bottom.
Step 4Turn the dough, flouring your fingers if necessary, into the pan and press it into the bottom and sides. Flute the sides. Smear the top with the apricot jam.
Step 5Cut the apricots in half and remove the pits. Press the apricots skin side down into the dough.
Step 6Place the pan on a baking sheet and bake until the kuchen is golden, 40 minutes.
Step 7Meanwhile, beat the egg whites on high speed until frothy, then add the remaining 1/4 cup sugar and beat until the whites form stiff peaks, 3 to 4 minutes.
Step 8Remove the kuchen from the oven and spoon the egg white mixture evenly over the apricots, spreading with the back of the spoon. Lower the oven to 325 degrees and bake until the top of the cake is golden, another 15 to 20 minutes.