Preheat the broiler to high. Arrange the slices of bread on a baking sheet and broil until golden brown on both sides.
Cut the chorizo slices to fit on the toasts. Set aside.
Heat a thin layer of olive oil in a large skillet over medium heat until a cube of bread sizzles. Break the eggs into the skillet and cook, spooning the fat over the yolks, until the whites are set and the yolks are cooked to your liking.
Remove the fried eggs from the skillet and drain on paper towels. Immediately transfer to the chorizo-topped toasts and dust with paprika. Season to taste. Serve immediately.