Heat the oil in a large nonstick skillet over medium-high heat. Add the onions and cook, stirring, until soft and lightly browned, about 6 minutes. Add the sage, garlic and jalapenos and cook, stirring, until fragrant, about 30 seconds. Add the courgettes, vinegar, 3/4 teaspoon salt and a few grinds of pepper and stir to combine. Cover and cook, stirring occasionally, until the squash begins to soften, 6 to 8 minutes. Uncover and add the red pepper and half of the parsley. Cook until the squash is completely soft and lightly brown, 6 to 8 minutes more. Remove from the heat.
Make 8 small indentations in the squash with a measuring cup or the back of a ladle. Crack the eggs into the indentations and sprinkle with salt and pepper. Return the pan to medium heat, cover and cook until the egg whites are set and the yolks are still runny, about 4 minutes.
Sprinkle with the remaining parsley and serve.