Heat enough oil in a pan to deep fry tortillas. Fry until golden color and crisp. Drain on a paper towel. Set aside.
Heat oil over medium/low heat and fry potatoes in a single layer until tender and golden. Drain oil from potatoes. Return potatoes to heat. Add chorizo to skillet; crumble meat as it cooks for about five minutes. Set aside and keep warm.
Salsa: Place all ingredients in a small sauce pot. Bring to a simmer and cook until vegetables are tender. Place in a blender jar and process until smooth.
Assemble tostadas.
Spread a half ounce of sour cream on each tortilla.
Top with about 2 tablespoons of potato/chorizo mixture, shredded lettuce, onion and tomatoes. Drizzle with a little salsa and sprinkle with grated parmesan.
Set three tostadas on a plate lined with the shredded leaf lettuce and add a small ramekin of salsa on the side.