Heat brown sugar, butter, heavy cream and salt in a saucepan over medium-high heat. Stir every 30 seconds until the mixture caramelizes and smells like caramel, about 5 minutes. Remove from heat immediately and let cool for 2-3 minutes.
Puree the bananas with an immersion blender. Add the cooled caramel and blend until smooth.
Mix mascarpone and yogurt together until smooth. Add 3/4 of the caramel-banana mixture and stir thoroughly. Transfer to a serving dish and smooth the surface. Pour the remaining caramel-banana mixture over the top as a topping.