Dissolve the yeast in the warm water in a large bowl. Whisk in the evaporated milk, sugar, salt and eggs.
Add 4 cups of the flour and beat with an electric mixer or in a stand mixer until smooth, and then add the shortening and beat until smooth. Add the remaining 3 cups flour and beat until smooth once again. Cover and refrigerate 24 hours. (If pressed for time, you can chill as little as 3 hours.)
Heat the oil to 350 degrees F. Preheat the grill to medium heat, 300 degrees F.
Roll the dough out 1/8-inch thick. Cut out donut shapes using the top of a drinking glass and cut out the holes using a butter knife. Fry the donuts, turning frequently, about 5 minutes, and then drain on paper towels. If the doughnuts do not pop up, the oil is not hot enough.
Slice the banana into 1/4-inch-thick pieces and place on the grill. Liberally pour an equal mixture of butter and honey on the banana pieces and sprinkle with cinnamon and sugar. As the bananas cook, the sugar will start to caramelize. Grill both sides until golden brown, but do not burn.
Fully coat the donuts with cream cheese icing, top with the hot caramelized banana pieces and sprinkle with several tablespoons of brown sugar.
This recipe was provided by a chef, restaurant or culinary professional and makes a large quantity. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.