In a skillet over medium-high heat, melt the butter; add the brown sugar and cook, stirring constantly to dissolve, for about 1 minute.
Add the pecans and continue to cook for 1 minute, then add the bananas and vanilla; now cook that for 1 minute.
Remove pan from the heat.
In a large mixing bowl, combine the beaten eggs, milk and baking powder to make a batter; add the flour, 1/4 cup at the time, beating until it all is used and the batter is smooth.
Now add the banana mixture to the batter and fold to mix.
In a pot that is deep enough to safely deep-fry, heat the shortening to 360F; season with cane syrup and cinnamon.
Drop the batter, a heaping tablespoon at a time, into the hot oil.
When the beignets pop to the surface, roll them around with a slotted spoon in the oil to brown them evenly.
Remove and drain on paper towels.
Immediately sprinkle the beignets with icing sugar (powdered sugar) and make sure you serve the beignets warm.