Preheat oven to 350ºF. Grease and line a 9x9 baking pan.
In a large bowl, beat butter and sugar together until light and fluffy, about 5 minutes. This can also be done using an electric mixer!
Add eggs one at a time and mix until incorporated. Stir in yogurt.
In a medium bowl, sift flour, baking powder, baking soda, salt and turmeric. Add into butter mixture and mix until just combined. Be careful to not over mix!
Next prepare the filling/crumb. In a medium bowl, mix brown sugar, cinnamon, ginger, salt and sesame until combined. Reserve 3/4 cup for the middle of the cake. Add flour and melted butter to the remaining mixture. Stir to form a crumble.
Spread half of the turmeric batter on the bottom of the 9x9 baking pan. Sprinkle the reserved 3/4 cup brown sugar mixture all over. Top with remaining half of batter and spread out evenly.
Top cake all over with crumble. You may have a bit leftover. I just like a lot of crumble haha!
Transfer to oven and bake for 35-45 minutes until a toothpick inserted comes out clean. Check in multiple spots with toothpick as the cake can seem deceivingly cooked!