Heat the oven to 180°C / 350°F. Grease a 6-cup muffin tin or popover pan well, including the rim — the batter climbs while baking and sticks if the rim is bare.
Whisk the flour, sugar, baking powder and salt together in a bowl.
In a separate bowl, whisk the batter egg, milk and oil until smooth, then pour into the dry ingredients and stir just until no dry flour remains. A few small lumps are fine.
Fill each muffin cup about two-thirds full with batter.
Crack one whole egg directly on top of the batter in each cup. Don't stir it in.
Scatter on any savory toppings now, if using.
Bake 18 to 20 minutes, until the batter around the egg is set and lightly golden and the egg white is fully opaque. Check at 16 minutes if you want the yolk to stay soft.
Let the tin sit 3 minutes before unmolding — the bread is fragile straight out of the oven and tears at the sides if rushed.