1. Preheat your oven to 190°C/Fan 170°C/Gas 5. Put a large pan of water on to boil. Scrub the potatoes and quarter them. Chop them into long chunks, around 1cm thick. When the water is boiling, add the vinegar, a big pinch of salt and the potatoes. Simmer for 10 mins till the potatoes are starting to soften. Drain well.
2. While the potatoes cook, peel and finely slice the shallots. Peel and crush the garlic. In a small pan, warm ½ tbsp oil. Add the shallots and season them with a pinch of salt and pepper. Cook and stir for 5 mins till the shallots start to brown and look glossy. Stir in the garlic, tomato purée, smoked paprika, chilli flakes, tamari, sugar and the leaves from a few sprigs of thyme.
3. Drain the cannellini beans and add them to the pan with the passata. Cover and simmer for 10 mins till the beans thicken a little. Take off the heat and set aside.
4. The potatoes should be ready to drain by now, so make sure they are drained and leave them in the colander to cool for a few mins. Halve the pepper and slice it into long, thin strips, discarding the seeds and white pith. Peel and thinly slice the red onion. Quarter or halve the mushrooms.
5. Arrange the vegan sausages and cherry tomatoes on a baking tray. Slide them into the oven. Bake for 15 mins.
6. While the sausages roast, warm 2 tbsp oil in a deep frying pan. Tip in the potatoes. Fry for 8-10 mins, turning often, till the potatoes are golden brown all over. Lift out of the pan and pop on a plate.
7. Warm another 1 tbsp oil in the pan. Add the pepper and onion. Stir and fry for 3 mins to just start to soften the veg, then add the mushrooms. Stir and fry for 5-6 mins till the veg are tender. Add the thyme leaves to the pan and fry for 1 min, then return the potatoes to the pan. Season with a pinch of salt and pepper and toss to mix.
8. Pop the beans back on the heat for 1-2 mins to warm through, if necessary. While they heat up, arrange the home fries on two warm serving plates. Add the sausages and tomatoes to the plate. Spoon on the beans and serve.