Beat eggs until ropey and pale yellow (about 4 minutes), using flat blade of stand mixer; add olive oil and incorporate. (If you don’t have a stand mixer, beat for 6–7 minutes with small mixer or a whisk; the paler the eggs become, the loftier and more tender the cake will be.) The cake will only be successful if the eggs are very thoroughly beaten.
Add citrus zest and sugar, then ground almonds and baking powder.
Whisk until combined; pour into oiled spring-form pan.
Bake until straw or cake tester inserted in center of cake comes out clean, roughly 40–60 minutes. Check frequently toward the end of baking.
Squeeze ½ cup of lemon juice, add it to ½ cup of sugar in a small saucepan, and cook only until the sugar has completely melted.
Spread across the top of the cake thinly; in a minute or two, add another layer; keep doing this until you’ve used up all of the syrup.