Fry the onions in 1tbsp of oil until soft then add the garlic and smoked sweet paprika. Continue to fry for another 30 seconds.
Put the fried onion mixture in a food processor along with the beans, breadcrumbs and cheese, and season with salt and pepper. Whizz until the mixture becomes a paté consistency.
Form and roll the mixture into 8 sausages. Dip each one in the beaten egg and then roll in the extra breadcrumbs. Shallow fry the sausages two at a time, turning only when the bottoms have browned first to avoid their falling apart. (*If making the vegan version, coat in the nuts and grill under a moderate heat, turning occasionally.) This should take around 8 minutes.
While the sausages are cooking prepare your mash by boiling the vegetables for 20-25 minutes, or until soft. Drain and mash thoroughly. Stir in the butter or vegan margarine and horseradish.
Serve the sausage with the mash, peas, broad beans and your favourite onion gravy.