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Set the oven to 350F
Beat the butter and sugar together for several minutes until smooth and fluffy. Beat in the egg and vanilla.
Mix in the mashed banana, and then the flour and salt. Mix just until everything is well blended, don't over mix.
Spread into an 9x9 square baking dish. I like to spray the dish with baking spray and also line it with parchment paper with long ends so I can lift it out to frost and cut it easily.
Bake for 25 to 30 minutes, until the center is set. I check with a toothpick.
Let the cake cool most of the way before you make the frosting.
To make the caramel frosting put the butter, brown sugar and milk or cream in a small saucepan and melt the butter, whisking all the time. Continue whisking until the mixture comes to a boil, then turn off the heat and add the sifted powdered sugar, whisking until completely smooth. You may need to add a little bit more powdered sugar if it seems very thin.
Spread it immediately onto the cake, it will set up very quickly.