Mash your roast potatoes with the bean water to loosen them up a little. We used an immersion blender, but I … might not advise that with sweet potatoes, as it jammed up way more than with regular potatoes. Mix in the veg first, then the cheese, and finally 1/2c breadcrumbs. Taste it. Add salt and pepper as needed.
Take the other 1/4c breadcrumbs and dump it on a plate.
And now? The messy part. Stick your hands in it and knead the fuck out of it, until the breadcrumbs are more or less evenly distributed, and they’ve absorbed a decent amount of the damp. Once you’ve got something relatively doughy-feeling, grab lumps and squish them into roughly palm-sized patties, a little less than 1 cm thick. Dip them in the breadcrumbs so both sides are coated, then set them aside.
Coat the bottom of a fry pan with oil and heat it to the closest thing your range offers to ‘medium-low’, which is to say do not turn it up to extra high, like we did. *coughcough* Put a few patties in the pan at a time and cook ~5 minutes, then flip with a spatula and cook another 5m. Ish. What you’re looking for is for the surface to become lightly browned. When you hit that point on both sides, you’re done. (Unlike us. We burnt them in like 2m. Don’t be us, kids.)
We ate them with ketchup, and they were quite tasty, but your taste in dressing may vary. Honey-mustard might not be horrible.