Add the walnuts to a food processor, and blitz to form a coarse crumb. Add the drained black beans, pickled jalapeño slices, and half of the tortilla chips. Also add the smoked paprika and a good pinch of salt and pepper. Blitz again until well combined.
Crush the remaining tortilla chips, and add them to the mixture. Mix by hand to combine.
With clean hands, form the mixture into three large patties.
Heat a dash of oil in a frying pan, and add the black bean burgers. Cook over a fairly low heat for around 5 minutes each side, until crispy on the outside and piping hot in the centre. You can cover the pan with a lid if the burgers need help cooking through to the centre.
Meanwhile, make the nacho cheese sauce. Melt the butter in a small saucepan, and add the flour. Mix well to form a roux, and cook for 1 minute over a very low heat. Add the milk 1 tbsp at a time, stirring until the mixture is smooth each time before adding more. When the mixture has formed a smooth sauce, add the chopped jalapeños, American cheese and a pinch of cayenne pepper. Stir thoroughly until the cheese has melted and formed a thick cheese sauce. Season to taste.
Assemble the burgers in buns with the nacho cheese sauce, salsa, mashed avocado and more slices of jalapeño.