Coarsely grate the beetroots, roughly chop the basil, finely chop the onion and garlic and place in a large mixing bowl with the oats and oil. Crack in the eggs, crumble in the feta, season to taste and mix to combine. Cover and put in the fridge for at least 30 minutes or until the oats have absorbed the liquid.
Using your hands, shape the mixture into 6–8 large patties. Heat 1 tablespoon of oil in a large non-stick frying pan (skillet) on a medium-high heat. Fry the patties for a few minutes or until the base is golden. Carefully flip with a spatula and fry the other side.
Alternatively, bake the patties in the oven at 200°C (400°F/Gas mark 6) for 20 minutes, flip and bake for a further 5–10 minutes or until golden on both sides. Or put them on the grill.