Heat oil in a deep saucepan to 180C. Pound paprika and 2 tsp sea salt in a mortar and pestle until finely ground, then set aside.
Stack tortillas on top of each other, cut into 8 wedges, then deep-fry in batches, turning occasionally, until crisp (1-2 minutes; be careful, hot oil will spit). Remove with a slotted spoon, season with paprika salt, then cool. Tostadas will keep for 3 days in an airtight container.
For rough guacamole, pound garlic, chilli and coriander roots in a mortar and pestle to a coarse paste. Add avocado, tomato, onion and lime juice, pound to combine, then stir in oil and coriander and season to taste. Serve with tostadas.