Preheat the oven to 450°F. Put the tots on a baking sheet and toss with oil, salt and pepper. Cook in the oven for about 25 minutes until crispy and browned.
Remove the skin and seeds from the avocados and place the flesh in a large bowl. Add in the lime juice, garlic and salt and pepper and stir/mash to combine. Cover with plastic wrap so the wrap is touching the top of the guac. Set aside in the fridge until ready to use.
Make the cheese sauce – Whisk the corn starch into the evaporated milk. Pour this mixture into a small sauce pan. Bring to a simmer, stirring often. As it comes to a simmer you will see it thicken up. Remove from heat and stir in the cheese. Continue to stir and the residual heat should melt the cheese, but if not, you can put it on low heat, just keep an eye on it because it will separate if it gets too hot. Hold this over as low of a heat as you can until ready to use, adding a splash of milk if it gets too thick. (“alt” milk will work here if that is all you have.)
Preheat the grill to medium-high heat. Toast the buns on the grill first for about one minute. Remove from heat and set aside. Smear about 1 tablespoon of sour cream on each bottom bun.
Next, grill the burgers about 5 minutes on the first side, until you start to see the juices collecting on the top of the burger. Flip and add the cheese slices. Cook another 5 minutes until it is cooked through.
Put the burgers on the bottom buns, then spread on the guac. Pile up some tots, then pour on the cheese sauce. Finally top with a few jalapeño slices, add on the top bun, and serve.