Fill a large pot three fourths full with cold water and bring it to a boil, set over high heat. In the meantime, prepare the potatoes.
Wash and scrub the potatoes well to remove any dirt, and then remove and discard any "eyes" or stems; don't peel potatoes, since the skins add an extra flavour (and crisp) to them. Cut the potatoes into 2, going down through the narrowest side. If necessary, remove and discard any black or discoloured parts found in them. Then cut each part into 6 - 8 lengthwise wedges, by placing the potato part upright and then slicing downward, going from the top through to the bottom. Repeat with remaining potatoes in the same manner and place them in colander: rinse.
When the water has come to a boil, stir in the chicken base powder. Then drop in the potato wedges and stir them around for a few seconds. Boil the potatoes for 8 minutes; starting from the time the water has returned to a boil. Stirring them occasionally using a slotted ladle. Don't boil them longer than that, because they will break apart. Boil potatoes longer only if you've sliced them into thicker wedges. In either case, though, potatoes are ready when their skins are just beginning to peel off of them.
As the potatoes are boiling, place an oven rack in the middle position and preheat the oven to 425'F. Cut a piece of parchment paper to fit up the sides of a baking sheet (jellyroll pan) by at least 1 inch. This makes cleanup a breeze later on.
Remove the potatoes from the boiling water using a slotted ladle and transfer them to a large mixing bowl. Don't worry about the water that you carry over with the slotted ladle, since this adds a little moisture to them and helps in mixing up the flavourings. Don't drain them in a colander; otherwise, this may break up the wedges. To the potatoes, add in the Cajun spice mix, onions soup mix, salt and oil.
Lay out the wedges in the prepared baking sheet, in a single layer and then bake them for 30 minutes, for tender potatoes, or 45 - 50 minutes for crispy ones. In either case, though, halfway through the baking time, turn them over using a spatula. After the total cooking time of your choice, remove them from the oven and sprinkle your choice of the cheese over them. Then bake them for another 5 more minutes or so, long enough to heat up and slightly darken the cheese. Transfer to serving platter and serve.