Heat canola oil in a large pan.
Peel plantains and slice crosswise into fourths.
Fry plantains in the heated oil until slightly golden, about 5 minutes.
With the bottom of a bottle, small pan or tostonera if you have one, press on the plantains to flatten them to about half their original size into a disk, then shape the disk into a small cup.
Return the plantain cups to the hot oil, and fry until golden and crisp, 5 to 7 minutes more. Remove from the oil, place on a paper towel and sprinkle with salt. Set aside.
Fill the plantain cups with the shredded beef and top with mayo and ketchup, if desired.