For the dough, measure all the ingredients except the cream cheese and butter into a bowl and stir with a wooden spoon, or blend in a stand mixer fitted with the hook attachment until evenly combined. Beat in the cream cheese and butter until blended. If mixing by had, turn the dough out onto a work surface and knead until smooth, about 5 minutes, or if in a mixer, knead for about 3 minutes. Transfer the dough to an oiled bowl, cover with plastic wrap and let rise until doubled in size, 90 minutes to 2 hours.
For the caramel, bring the water, sugar and lemon juice to a boil over high heat and continue to boil, uncovered and occasionally brushing the sides of the pot with water, until it turns a light amber colour. Remove the pot from the heat and carefully whisk in the cream and butter (watch out for the steam). Once the caramel stops bubbling, whisk in the vanilla and cinnamon. Spoon half of this mixture into 12 greased muffin cups or 12 greased ramekins. While the caramel is still warm, stir in the mashed banana and set aside until the sticky bun dough is ready to assemble.
Once risen, turn the dough out onto a lightly floured work surface and roll it into a rectangle 12×18-inches. Spread the banana caramel filling over the dough (the filling will be very soft) and sprinkle the walnut pieces overtop. Roll up the dough from the 18-inch side and cut into 12 buns. Place the buns into the prepared tins or ramekins (and if any filling squishes out, it can be spooned on top of the buns), cover with plastic wrap and let rise for an hour.
Preheat the oven to 350°F. Uncover the buns and bake them for 25 to 30 minutes until they are a rich golden brown. Allow the buns to cool for 15 minutes before frosting.
For the frosting, beat the cream cheese and butter until fluffy and then beat in the icing sugar. Beat in the white chocolate and vanilla and spread or dollop this on top of each sticky bun and serve.