Heat a thin layer of olive oil in a medium frying pan over a medium heat. Add the onion and cook, stirring, for about 5 minutes until softened. Add the garlic and cook for 1 minute more. Remove from the heat and set aside.
In a large bowl, combine the flax seeds with 6 tablespoons water and let stand for 10 minutes.
Meanwhile, in a food processor, process the oats until they are finely chopped and bordering on a flour-like texture. Add the black beans to the food processor and pulse until they’re finely chopped and combined with the oats, but not puréed.
Put the processed oats and black beans, grated beetroot, cooked onions and garlic, tomato purée, smoked paprika and oregano into the large bowl with the flax seeds. Season with salt and pepper and mix with a rubber spatula or with your hands until everything is well combined. Form the mixture into 6–8 patties using damp hands, making them about 2.5 cm/1 inch thick and about 7.5 cm/3–4 inches wide.
In a large frying pan, heat enough oil to cover the base over a medium-high heat. Add two patties and cook for 3–4 minutes on one side, until browned and firm. Flip and cook for another 3–4 minutes on the other side. Reduce the heat to medium if the patties are getting too charred. Remove and repeat with the remaining burgers.
Alternatively, you can lightly brush the burgers with oil and bake them on a baking tray lined with parchment paper for 25 minutes in an oven preheated to 200°C/400°F/gas mark 6, flipping them halfway through the cooking time.
Serve warm on toasted English muffins or buns with plenty of your chosen toppings.