In a large pot, bring milk, 3 cups water, chile powder, pepper, cumin and salt to a simmer.
Reduce heat. Add polenta and stir with a fork to remove lumps.
As polenta starts to thicken, add half of the queso blanco, reserving the rest in the refrigerator. Stir until cheese starts to melt. Turn off heat and allow to rest.
When cool enough to handle, spoon mixture out onto plastic wrap. Shape into a tube 2 to 3 inches thick and wrap. Refrigerate overnight.
In a frying pan, heat oil until ready for frying. Remove polenta and queso blanco from the refrigerator.
Unwrap the polenta and slice the tube into 10 to 12 ½-inch-thick slices. Add 5 to 6 slices to pan and fry until golden brown on one side. Flip and fry on the other side. Remove and drain on paper towels. Repeat with the remaining slices.
Arrange 2 to 3 polenta patties per plate. Top with chopped avocado and the remaining queso blanco. Sprinkle with nuts or seeds, then garnish with cilantro. Salt and pepper to taste and serve immediately.