Just for kicks, put out a request for bids.
Why not melt a nickel-iron asteroid, inject a bubble of air into the center, and then spin it to create centripedal force.
That, combined with the air pressure from the inside... and none from the outside, would then spin a nickel-iron bubble, which would then cool into a hollow sphere.
Which would be the external armor/skin of a Death Star. All you’d then need to do would be to cut a whole into it and then start working on the insides.