Prepare the Pan:
Preheat your oven to 350°F (175°C).
Grease and line a 9-inch cake pan with parchment paper.
Mix the Dry Ingredients:
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Cream Butter and Sugar:
In a large mixing bowl, use an electric mixer to cream the softened butter and sugar until light and fluffy (about 2–3 minutes).
Add Eggs and Vanilla:
Beat in the eggs, one at a time, followed by the vanilla extract.
Incorporate the Dry Ingredients:
Gradually add the dry ingredients to the wet mixture, alternating with the yogurt (beginning and ending with the dry ingredients). Mix until just combined.
Add Mulberries:
Gently fold in 1 cup of the mulberries, being careful not to overmix to avoid staining the batter excessively.
Bake the Cake:
Pour the batter into the prepared pan, spreading it evenly. Scatter the remaining ½ cup of mulberries over the top.
Bake for 35–40 minutes, or until a toothpick inserted into the center comes out clean.
Cool and Serve:
Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Dust with powdered sugar before serving, if desired.