Set a rack in the middle of the oven and preheat to 350F. Line an 8-inch cake pan (that’s at least 2 inches tall) with parchment paper and/or oil.
In a medium-sized mixing bowl, whisk sugar and skyr together until combined. Mix in eggs, oil, milk, and vanilla extract, and stir until homogeneous.
Whisk in the kosher salt and baking powder until combined. Slowly mix in the flour, gently folding after each addition until no dry clumps remain.
Pour batter into the cake pan, and bake for 25 to 30 minutes, or until a toothpick inserted into the center of the cake comes out clean (a few small crumbs are okay).
Let cake cool for 10 minutes, then run a knife around the edges and remove from the pan onto a cooling rack. Squeeze a bit of lemon juice onto the top of the cake – this adds a bit of lemon flavor and moistens the cake. Let the cake fully cool before drizzling glaze on top.
Wash and wipe the mixing bowl clean, then whisk in the lemon skyr until smooth. Slowly add the sifted powdered sugar until a glaze forms; feel free to add as much or as little of the powdered sugar as needed to reach your desired consistency. It will have a slightly looser feel than a traditional glaze, but should still coat the back of a spoon. You may need to squeeze in additional lemon juice to maintain the tart flavor.
Slowly drizzle the glaze over the cooled cake. Top with lemon zest and candied lemon (if using). Keep refrigerated.