Lidgar
Gongfarmer
Out of curiosity, how much more basic do you want? What do you want from a B-series-compatible basic game than the current basic doesn't deliver?
Sure. Really it is just three rather minor things:
1. Races (dwarves, elves, halflings, and gnomes, because, gnomes) as classes. Humans get to choose from the basic four.
2. A more generic Wizard class. The evoker arcane tradition is a little too fiddly/specific for me.
3. A "B" series of adventure modules, not unlike what is included in the Starter Set.
You might be interested in Rogue Comet's Dungeonesque. In the opinion of many, it's a better 5e Basic than 5e Basic is. Though as @Mouseferatu's question touched upon, a lot will depend on what, exactly, you're looking for.
I looked at that and the reviews I have seen are less than complimentary for the price. Would be interested to hear from others who have tried it.
Again, I have home-brewed this well enough for now. Although I continue to tweak. Eventually will post here and DMG.