To make the 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 2 cups of the boiling water into a small saucepan, bring back to a boil add all the lemon rind, and boil for 30 seconds. Drain in a strainer and rinse the rind under cold running water. Repeat 2 times more, using fresh boiling water each time.
Combine the sugar and 2 cups of tap water in the saucepan and bring to a boil. Add the blanched rind and reduce the heat to a simmer. Simmer the rind until tender, about 1 hour. Drain the rind in a strainer (reserve the sweet, lemony syrup for sweetening drinks, if you like). Arrange the strips on a wire rack, using your fingers to gently spread them out so that they do not touch each other. Let them cool and store them in an airtight container.
To make the cake: Heat the oven to 375 degrees F.
Sift the sifted cake flour with 1/2 cup of the sugar 3 times (this is to aerate the mixture and make it lighter). 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 the egg whites are stiff and the sugar is dissolved, about 30 seconds more.
Fold the sifted flour-sugar mixture into the whites by hand just until incorporated. Fold in the lemon zest and vanilla extract.
Spoon or pipe the batter into the cups of the ungreased mini muffin tin, filling the cups until almost full (they will not expand much). Bake until the cakes are light golden brown, 12 to 16 minutes.
Let the cakes cool in the tin, then run a butter knife around the edges to cut the cakes free, leaving the browned walls and bottom of the cake in the pan. Remove the cakes from the tin and place on a wire rack set over a sheet pan.
To finish the dessert, stir the glaze ingredients together until smooth, Turn the cakes over to the brown top becomes the base. Dip the new top (the white side) of each cake into the glaze, then carefully place it on the wire rack, glaze side up, to set.
Chop the lemon confit (you may not need all of it) and make a little mound of chopped confit in the center of each cake. Let the glaze set for 30 minutes before serving the cakes.