Humankind has yearned for hundreds of thousands of years to explore and truly understand the dynamics of our enigmatic universe. However, we have often been limited by our hindsight here on Earth, or the limitations of human travel to further destinations. Having the ability to send humans to deep space would arguably set us millions of years ahead in our scientific understanding of various physical processes, including insight on some of the key mysteries that we still face. Perhaps a settlement further away from the Sun, Earth, and limiting optical resolution could provide us with greater ability to collect more meaningful data through our telescopes or other instruments. Moreover, one of the most significant abilities of such a settlement could be slightly easier access to sites of research within our own solar system that could be essential in the forthcoming years, such as Jupiter, Titan, the Kuiper Belt, and some Oort Cloud objects. Here we describe a unique option and set of goals to pursue and achieve just that via a mission to an L5 Trojan asteroid of Neptune, 2011 HM102. In this paper, we propose a number of possible challenges presented by traveling to the base, modeling its layout, maintaining the presence of life, and opportunities for research on the asteroid as well as possible solutions to these challenges. We begin our journey by outlining some motivations for creating a settlement on the asteroid, then outline a few key technological goals that must be achieved before we are capable of efficiently sending a colony of people to the settlement. We describe materials necessary for its construction as well as a novel mechanism for artificial gravity utilizing the Roche limit of the asteroid and multiple applications of quark-gluon plasma. From there we explore more aspects of settlement design, including key considerations for the layout of our settlement, sources of power, and protection from high-energy radiation from sources such as galactic cosmic rays. Then, we embark on a detailed discussion on the measures needed to maintain life on the settlement, such as hydroponic crop growth, a cycle for water recovery and oxygen generation, temperature maintenance, and air purification. Some remarks on the sustainability of life on the settlement follow, as well as some recommendations for entertainment, social life, economics, and governmental systems on the settlement.