wolfyvegan

Syntropic agriculture practices achieve this and some semblance of a forest at the same time. Chop and drop. Smother the grass with mulch.

As others have suggested, shade out the bullshit with a diverse array of fruit trees and other useful vegetation in order to reclaim the land and grow an abundance of food at the same time. Even if you can't devote much time and energy to it, planting some vigorous (ideally native) pioneer species and hardy fruit trees and then just tossing seeds in there on a regular basis will go a long way toward exterminating the grass. I also second the recommendation of clover as a groundcover.

Properly scaled up, this type of community reforestation effort could work.

But if you don't plant trees, there will continue to be droughts, as trees help to regulate humidity and precipitation. Farmers in drought-prone areas actually plant trees (agroforestry) in order to reduce crop losses due to drought. Even in urban areas, planting trees (especially natives) can have many benefits for reducing the impact of drought. Of course, a diverse forest ecosystem would be most resilient.