For the non-hugel bed,you could consume the "lasagna" method, covering the area with cardboard, or wetting the cardboard thoroughly,then putting compost and mulch on top of the cardboard (at least 2-3 inches of each). Then just poke holes in the cardboard and plant into the soil beneath. The cardboard will smother the grass, which will decompose into the soil, and the cardboard will disintegrate over the course of a few months,further feeding the soil.
Source: thesurvivalpodcast.com