Place all bean paste ingredients into a food processor and blend to a rough paste — you want some texture, not a completely smooth purée. Taste and adjust seasoning.
Roughly chop all salsa ingredients and combine in a bowl. Stir, taste and adjust salt and lime juice. Set aside.
Spread 2 generous spoonfuls of bean paste evenly over one half of each tortilla, stopping about 3cm from the edges.
Scatter grated cheddar over the paste then fold the tortilla in half and press down firmly.
Heat a griddle pan or heavy frying pan over medium-high heat — no oil needed. Cook each quesadilla for 2-3 minutes per side until the exterior is lightly charred and crispy and the cheese has melted inside.
Slice each quesadilla into 2-3 wedges and serve immediately with the fresh salsa alongside and sour cream for dipping.