Preheat oven to 350F/175C/Gas 4.  Select your pan.  If using four large tortillas, select a pan that fits one tortilla with about 1/2" extra on each side.  If you do not have such a pan, select a larger pan and block off the rest with foil to make an opening the right size.  This prevents you from needing too much enchilada sauce later.  If using six smaller tortillas, select a pan that fits one tortilla in one direction and one and a half tortillas in the other direction, with about 1/2" extra on each side.  Again, make a pan fit these dimensions if you do not already have one, or use two smaller pans.

Mix together chicken, onion, cumin, and cream cheese in a large bowl; set aside.  Place about 1/4 cup enchilada sauce on the bottom of the pan, tilting until surface is covered.  Set aside.

Place oil in a skillet that is larger than your tortillas, at least 1" deep.  Heat oil to 360F.  While oil heats, set tortillas on a plate on one side of pan, an empty plate on the other side of the pan, and get out a pair of tongs.  When the oil is ready, place one tortilla in the oil, pushing down with the tongs to immerse it.  The tortilla may bubble in places, this is fine.  After about 30 seconds it will be done; lift out with the tongs, holding vertically over the oil to let the excess oil drip off, while placing the next tortilla in the oil.  You should only need to let it drip for about 3 seconds, then place it on an empty plate.  Repeat until all tortillas are cooked.

Once the tortillas are ready, work quickly.  Place one-fourth or one-sixth of filling on one tortilla, about one tablespoon of shredded cheese, spread into a line, and roll the tortilla into a cylinder.  Do not try to tuck the ends closed, just leave them open.  Place in prepared pan, seam side down.  Repeat until all tortillas are filled.  Cover with enchilada sauce, then sprinkle the remainder of shredded cheese on top.  Cover with foil.

If desired, you can stop here and put it in the fridge until you're ready to bake.

Bake for 25 minutes.  Remove foil, and bake for an additional 5 minutes.  Serve and enjoy!