Preheat oven to 350°F. Grease an 8" round pan, preferably one with a removable bottom (a springform pan will also work) and line the bottom with parchment.
Add the butter, sugar and zest to the bowl of stand mixer and with the whisk attachment, beat until light and fluffy.
Add the eggs one at a time, adding 2 tablespoons of flour with the last egg, whisking until incorporated.
Sift the flour over the bowl, add 2 tablespoons of hot water, then fold in gently until no dry flour is visible.
Spoon the mixture into the prepared pan, smoothing the top. Bake for 45–50 minutes. The cake should be shrinking away from the sides of the pan and a toothpick inserted into the center of the cake should come out clean. Remove from the oven and cook in the pan for about 5 minutes.
Mix the lemon juice and elderflower cordial together.
Using a fine skewer, poke holes all over the surface of the cake then pour the lemon/elderflower syrup evenly over the top followed by an even sprinkling of sugar. The sugar should sink in but still leave a crunchy crust.
Cook completely in the pan before removing.