Heat the oil in a saucepan and cook the onion over a medium-low heat until soft. Don’t rush this because you’re putting together the ingredients that will make tinned beans seem like more than just tinned beans: the onion and, especially, the olive oil. It will take 7-10 minutes to do this.
Add the garlic and cook for 2 minutes, then add the tomatoes. Cook these until they’re soft – another 5 minutes. You can crush them with the back of a wooden spoon to help them collapse. Season and add the thyme and the drained beans.
Cook the beans gently, stirring them every so often, for about 6 minutes – the important thing is that the beans suck up the flavours of the other ingredients. Check again for seasoning. Stir in the parsley. Cover to keep warm.
Heat 2 tbsp of the extra-virgin olive oil in a small frying pan and fry the eggs, spooning the hot fat over the yolks. Toast the bread. Halve the remaining garlic clove and rub it over the toast – the scratchy surface of the toast should help the garlic to flavour it.
Spoon the warm beans over the slices of toast, top each plateful with an egg – adding the warm oil from the pan – and grind some black pepper over the top. Grate on some Parmesan and serve immediately.