Preheat the oven to 325 degrees F. Line a 9" cake pan with parchment paper.
In a medium bowl, combine the flour, baking powder, and salt. Set aside.
In a large bowl, combine the sugar and lemon zest. Rub them together with your fingers until the it resembles wet sand and the zest smells aromatic.
Add the olive oil, lemon juice, eggs, and vanilla. Use an electric hand mixer or whisk to mix until well combined.
Add the dry ingredients and mix until fully combined.
Arrange the candied lemon slices in the cake pan, overlapping them slightly.
Very slowly pour the cake batter into the pan, careful not to disturb the lemon slices.
Bake the cake for 45-50 minutes or until lightly golden on top and a toothpick inserted comes out clean.
Once the cake comes out of the oven, use a knife to loosen the sides from the pan. Place a large plate on top and flip the cake over. Remove the pan, then gently peel back the parchment paper.
Allow the cake to cool completely, then use a serrated knife to cut individual slices, and enjoy!