Under the Research tab on the F2 (economy) screen, I researched the Asteroid Mining Module technology, and that research project just finished. I expected that I would then be able to design an asteroid mining component on the Design screen (Design button from F2 screen) but no such component seems to be there. There is also no such component when I bring up the Class Design screen.
So, how do I design and build a ship capable of extracting minerals from asteroids?