Cake: Preheat the oven to 375 degrees.
Sift the sifted cake flour with 1/2 cup of the sugar 3 times (this is to aerate the mixture and make it light). Set aside. Whip the egg whites in a mixer fitted with a whisk attachment until foamy. Add the cream of tartar and salt and continue whipping until soft peaks form. With the mixer running, gradually add the remaining cup of sugar and continue whipping until stiff and the sugar is dissolved, about 30 seconds more. Gradually add the sifted flour-sugar mixture and fold into the whites. Lastly fold in the lemon zest and vanilla extract. Pipe the batter into ungreased mini muffin tins. Bake until light golden brown, 12 to 15 minutes. Let the cakes cool in the pans, then run a knife along the edges to loosen them. Remove from the pans and place upside-down on a wire rack set over a sheet pan. Stir the lemon juice and powdered sugar together until smooth, creating a glaze. Pour over each cake until the tops are smoothly coated.
Confit: Cut a slice off the top and bottom of each lemon to expose the flesh. Cutting from top to bottom and following the contours of the fruit, cut off the peel and white pith in 1-inch-wide strips. Scrape off any pulp adhering to the strips, but leave the pith intact. You now have several 1-inch wide strips of lemon peel and pith. Cut each one into long strips, about 1/4-inch by 3 inches each. Meanwhile, boil a kettleful of water. Pour about a quart of the boiling water into a saucepan, bring to a boil, add all the lemon rind, and boil 30 seconds. Drain in a strainer and rinse under cold running water. Repeat 2 times more, using fresh boiling water each time.
Combine the 1 cup of sugar and 2 cups of water in a saucepan and bring to a boil. Add the blanched rind and reduce the heat to a simmer. Simmer until tender, about 1 hour. Drain in a strainer and let cool 15 minutes until cool enough to handle. Using your fingers, arrange the strips on a wire rack so that they do not touch each other. Let cool. Chop the lemon confit and sprinkle over the tops. Let set 30 minutes before serving.