Preheat the oven to 350°F (175°C). Grease a 9-inch round cake pan with butter. Melt 4 tablespoons of butter and pour it into the bottom of the pan, then sprinkle 1/2 cup of brown sugar evenly over it. Arrange the sliced ripe bananas in a single layer on top.

In a mixing bowl, cream together 1/2 cup of softened butter and 3/4 cup of granulated sugar until light and fluffy. Add 2 eggs one at a time, mixing well after each. Then mix in 1/2 cup of Greek yogurt until smooth.

In another bowl, whisk together 1 1/2 cups of all-purpose flour, 1 teaspoon of baking powder, 1/2 teaspoon of baking soda, and 1/4 teaspoon of salt. Gradually add this dry mixture to the wet ingredients, mixing gently.

Pour the batter over the arranged bananas in the cake pan, and spread evenly. Bake for 55-60 minutes or until a toothpick comes out clean.

Allow the cake to cool in the pan for 10-15 minutes. Run a knife around the edges and invert the cake onto a serving plate.

For the glaze, heat 1/2 cup of brown sugar and 1/4 cup of heavy cream in a saucepan over low heat until thickened. Drizzle over the cooled cake.