Yogurt Lemon Poundcake with Cardamom Glaze

My husband made this cake from Shaya for my father's birthday, and it is quite delicious.

½ pound (2 sticks) unsalted butter, softened, plus more for the pan
3 ½ cups cake flour, plus more for the pan
1 ½ teaspoons baking powder
½ teaspoon Morton kosher salt
3 ½ cups sugar, divided

1 lemon

1 cup full-fat Greek yogurt, room temperature, plus more for serving
4 eggs
6 egg yolks

1 teaspoon vanilla extract
1 cup water
1⁄4 cup extra-virgin olive oil, plus more for serving
8 cardamom pods, crushed
2 cups blackberries, halved 

1.  Heat the oven to 350 ̊F. Generously grease and flour a Bundt or tube pan. 

2.  Sift the cake flour, and combine it with the baking powder and salt. 

3.  Add 2 ½ cups sugar to a large mixing bowl or the bowl of a stand mixer. Grate the zest of the lemon and rub all the zest into the sugar; reserve half of the lemon for the cake soak. 

4.  Add the butter and yogurt to the mixing bowl, and cream everything with an electric mixer or the paddle attachment of the stand mixer on high speed for 5 minutes. You want the mixture to be light in color, with plenty of air in it. 

5.  Add the eggs and the yolks one at a time, mixing between additions, followed by the vanilla. Don't worry: the batter will look broken and curdled, but that's okay. Gradually add the flour mixture, and beat on low until just incorporated. Scrape the batter into the prepared pan. Lift the pan a couple inches off the counter, and let it drop evenly; do this a few times, to get rid of any air bubbles in the batter. 

6.  Bake on the center rack for 50 to 60 minutes, rotating the pan once, after 30 minutes. The cake is ready when a knife comes out clean. 

7.  While the cake bakes, make the soak: Combine the remaining cup of sugar with the water and olive oil in a saucepan. Squeeze the lemon juice in, and drop in the lemon with the cardamom pods. Bring the mixture to a simmer, then cover and remove from the heat until the cake is ready. (The oil and water will stay separate, which is fine.)
8.  Once you've pulled the cake from the oven, let it cool for about 10 minutes; strain the syrup, and discard all the solids. 

9.  Use a thin knife to cut about sixteen deep slits all over the 
cake, then gradually pour the syrup all over, 1⁄4 cup at a time, pausing between pours to let each one soak in. Let the cake cool completely in the pan before inverting it onto a cake plate or cutting board. Serve each slice with a dollop of yogurt, a drizzle of olive oil, and a pile of fresh berries.