Halve the cherry tomatoes and slice the avocado. Heat half the olive oil in a frying pan over medium-high heat and briefly fry the tomatoes until they soften and release their juices; scoop them onto a plate.
Pour the remaining oil into the same pan and gently fry the eggs until the whites are set but the yolk is still runny.
Place the fried eggs beside the tomatoes and fan the avocado slices alongside. Tear the basil roughly and scatter it over, along with a pinch of salt and freshly ground pepper. Serve immediately, with the runny yolk acting as a creamy sauce over everything.