Preheat oven to 350 degrees F. Butter an 8-by-8-inch square baking pan; line with parchment paper (but leave parchment unbuttered).
To make meringue, whisk sugar with cream of tartar. Place egg whites in a clean mixing bowl or the bowl of a stand mixer fitted with the whisk attachment. Whip on medium speed until eggwhites form fine bubbles and hold soft peaks. Slowly add sugar, 1 tablespoon at a time, whipping about 30 seconds before the next addition. After 10 to 15 minutes the meringue should be thick and glossy and hold stiff peaks; when you rub some between your fingers you should not feel any grains of sugar.
If you have two mixing bowls, just trade the clean one onto the mixer and set the bowl of meringue aside; otherwise transfer the meringue to another bowl and then put the used mixing bowl back on the mixer (no need to clean it completely before proceeding with the next step).
In a small bowl, rub lemon zest with sugar until fragrant and evenly distributed.
In a mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, cream butter and sugar together until fluffy, 2 to 3 minutes. Add egg and mix until incorporated.
Mix baking soda in with sour cream; whisk baking powder and salt in with flour.
With the mixer on low speed, add half of dry ingredients to batter, followed by half of sour cream and all of the lemon flavoring, lemon juice, and vanilla. Scrape down the sides of the bowl, then mix in remaining flour, then remaining sour cream until just incorporated.
Spread batter into prepared pan. Dollop meringue on top, then spread evenly over top of cake, using the back of a spoon to make swoops and swirls.
Bake for about 30 to 35 minutes or until meringue is lightly golden brown and a long skewer inserted near the center comes out with a few moist crumbs attached.
Place pan on a wire rack to cool completely before lifting out of pan to slice. Cut into squares. Cake is best the day it is made, but will keep, refrigerated in an airtight container, for up to 3 days (though meringue will soften the longer it sits).