Preheat the oven to 325. Butter a 9-inch round cake pan, line the bottom with a round of parchment and lightly butter the parchment. Set aside.
In a small bowl, combine the flour, baking powder, baking soda and salt. Whisk to combine and set aside.
Place the 1 cup sugar in a stand mixer and zest your lemons into the sugar. Beat for a minute or two, which will allow the lemon zest to release it’s oils into the sugar and bring out a more lemony flavor to the cake. Add in the softened butter and beat on high speed for 2-3 minutes until soft and creamy.
Add the eggs, one at a time into the butter mixture, scraping after each addition. It really helps here if your eggs are room temperature (see note). Add in the vanilla, scrape the bowl again, and beat to combine.
Add half of the flour to the mixer and combine on low speed. Add all of the yogurt, and mix again until incorporated. Add the remaining flour and mix until just combined. Don’t overmix the batter. Pour into your prepared pan and place in the oven. Bake about 35 minutes (it could take a little longer), until the cake is nicely browned, it has pulled away from the sides slightly, and the top feels firm to the touch.
Let the cake cool in the pan on a rack for 10 minutes. Meanwhile, combine the lemon juice and remaining 1/2 cup sugar in a small saucepan. Warm until the sugar is just dissolved. Using a skewer, poke holes around the cake evenly. Spoon the lemon syrup over the cake evenly and let the cake continue to cool in the pan.
Once the cake is cooled, remove it to a serving plate. Top with berries, dust with powdered sugar if desired, and serve with whipped cream.
Cake will keep, covered, for 2 days.
Using room temperature eggs will result in a better batter. Otherwise, the butter can seize up from the cold of the eggs and become grainy. In a pinch, I place the eggs in a bowl of warm water for a few minutes before I crack them. It takes the chill off and allows them to incorporate more easily.