Vesta full mosaic
Vesta is the third largest asteroid in the Main Asteroid Belt by size, and second most massive after Ceres. It is about 330 miles in diameter (oblate-spheroid). Very much like a small planet, Vesta is differentiated, with a dusty crust, rocky olivine mantle, and solid iron core. It is heavily cratered, with two giant impact basins near the south pole. Also like Earth, its moderate axial tilt gives it seasons, and water ice is thought to exist beneath its regolith near the poles . It surface has been mapped and spectroscopically analyzed by the Dawn probe.


First, tons of molten nickel/iron (mined from M-type asteroids) and decaying radioactive elements are injected into the core through various drill sites, to restart the magnetic field dynamo. Then Vesta is covered with a sealed world-dome of a super strong but clear material (preferably self repairing) held up by columns in place of the drill sites. Next, thermonuclear detonations and focused solar mirrors  could outgass carbon dioxide and oxygen, directly from the compounds in the regolith. As a thin atmosphere forms, strong greenhouse gases can be pumped in to heat the asteroid enough to melt any underground ice deposits. It is likely more air and water would be needed (this depends on the volume of the enclosed worldhouse), so nearby comets or astroids could be mined for volatiles. Buffer gases like Nitrogen or Argon are harder to come by, may need to be exported from the the outer dolar system. Eventually droplets of water (likely beachball sized in the low-G) may condense on the worldhouse roof and fall as rain, turning craters and troughs into lakes and rivers. Once the regolith oxidises and settles, genetically modified bacteria, algae, and eventually plants and animals, can introduced to form a biosphere.

A project like this could only be feasible in the far future, but turning Vesta into a garden world could help miners of the asteroid belt become less dependent on food from Earth or Mars, or simply act as a reserve of species.