Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar together with an electric mixer on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the lemon zest and vanilla extract.
In a small bowl, combine the plain Greek yogurt, fresh lemon juice, and whole milk.
Alternately add the flour mixture and the yogurt mixture to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes. Then transfer to a wire rack to cool completely.
While the cake is cooling, prepare the lemon yogurt by stirring together the plain Greek yogurt, fresh lemon juice, honey, and lemon zest in a small bowl until smooth.
Serve slices of the lemon cake with a dollop of the lemon yogurt on the side.