Any construction gurus? Rake overhang addon.

[Festivito]

1940's house. The outside rafters are higher than the interior rafters such that the roof boards are INSET. Thus adding a rake overhang would have no continuous sheathing on top.

Wishing to add only a 4 or 6" rake overhang.

Would securing a couple of 2x6's to the outside rafters be sufficient?
Or, should the whole roof be overlayed with an additional layer of, say, 1/8 or 1/4" 4x8 sheets.
Or, other suggestion.

Muchly appreciate any response.