Please see final instruction for how to prepare and bake this cake at high-altitude.
Preheat the oven to 350 degrees F and grease a 9-inch springform pan with butter. Set aside.
In the bowl of your stand mixer with paddle attachment fixed (or with a handheld mixer), cream together the butter, 1/4 cup granulated sugar, and brown sugar until smooth and creamy, about 1 minute. Add the eggs, and mix until incorporated. Add the vanilla extract and Greek yogurt and again, mix until incorporated. Add the flour, baking powder, baking soda, and salt. Mix until no dry ingredients remain. Fold in the berries, and then pour the mixture into the prepared pan. Set aside.
In the bowl of your stand mixer with paddle attachment fixed (or with a handheld mixer), cream together the cream cheese and remaining 1/4 cup of granulated sugar until smooth and creamy. Pour the mixture on top of the cake batter and very carefully spread the cream cheese until most of the top is covered. This does not have to be perfect. Set aside.
Next, prepare the crumble topping. In a medium bowl, whisk together the brown sugar, flour, and cinnamon. Add the cold and cubed butter and using your hands, a fork, or a pastry cutter, cut the butter into the brown sugar mixture until it resembles very small pea-sized clumps. Sprinkle the mixture on top of the cream cheese.
Bake the cake for 1 hour or up to 1 hour and 15 minutes or until a toothpick comes out "semi-clean." Remove from oven and let stand at room temperature for 30-minutes before glazing.
Meanwhile, whisk together the confectioner's sugar, heavy cream, and vanilla extract and smooth. Add more heavy cream as needed to get a drizzly consistency. Once the cake has cooled, drizzle it with the glaze. Store the cake at room temperature for about a day or keep in the fridge for 4-5 days. It is best served day of bake. Enjoy!
If you are baking this cake at high altitude, simply add 1 egg white and decrease the amount of baking powder by half. Increase the oven temperature to 365 degrees F and bake for about 55min-1 hour, or longer as needed.