Preheat oven to 350 degrees F. Butter and flour an 8-inch round cake pan.
For the cake: In a large bowl, using an electric mixer, beat the egg whites to soft peaks. Add 1/2 cup sugar and beat until the mixture holds stiff peaks.
In a separate large bowl, beat the vegetable oil, the remaining 1/2 cup sugar and salt. Add the egg yolks 1 at a time. Add the chopped mint, lemon juice and lemon zest. Add the flour and mix until just combined. Set aside.
Slowly add 1/2 of the egg white mixture into the oil mixture. Using a rubber spatula, carefully fold in the remaining egg white mixture. Spread the batter into the prepared cake pan and bake for 40 to 45 minutes until a toothpick inserted into the middle of the cake comes out clean. Transfer the cake to a cutting board and allow to cool before slicing.
For the syrup: In a small saucepan, combine the sugar, water, lemon juice, and lemon zest over medium heat. Bring to a boil, reduce the heat, and simmer until the sugar has dissolved, about 5 minutes, stirring occasionally, Remove the pan from the heat and allow the syrup to cool, about 20 minutes.
To serve, spoon some of the syrup onto each small plate or shallow bowl and lay a slice of cake on top. Drizzle the cake with additional syrup and garnish with a small sprig of mint.