Hi @Caroline and @nmgraham
It strikes me that this topic could potentially be a massive challenge in the sense that there are so many factors that could be considered in its scope. For example:
- Policy, regulation, law and governance
- Paradigm shifts in the socio-economic model
- Scenarios for the short and long term, and for different global and local cases
- Access to resources (including land, water and energy)
- Environmental impacts to land, water, air and climate
- Innovation and new technologies
So I reflected on what XPRIZE challenges are well known for and focused my thoughts primarily on the latter point, with a few references to other points where it seems relevant to the following.
A Generic Sustainable Cycle
This concise diagram illustrates how any product (or food) could be created from a basic set of resources by a creation process that assembles the product. In nature plants use nutrients, water, carbon dioxide and energy (from sunlight) to assemble a vast range of molecules that form the plant, and give rise to food. In nature every aspect, including byproducts, are recyclable. We humans use processes to manufacture and construct things but each step may require extra resources (outside the circle) and create pollutants [shown by the arrows attached to each box]. When a product reaches the end of its life some parts may be collected and recycled (or disassembled into basic components and resources).
Note: for a fully self-sustaining cycle there would not be any external resources, no pollution and no unrecoverable waste. In reality, our processes are imperfect. [Perhaps we can learn from nature.]
A fantastic but audacious opportunity exists here for an XPRIZE that copies another Star Trek technology: the Replicator! Okay we’re not in the 23rd century and so we might struggle for an exact copy; but within this decade it might well be possible to push 3d printing to the nano-scopic level [in fact some aspects already exist]. Such a device might take a set of atoms or molecules and assemble complex products, and foods. A related device might take waste and disassemble it back into (valuable) resources. If we could achieve this for food then each household might be able to take basic (readily available) raw materials and use this new device to create food. This removes most of the waste and pollution currently associated with the food (and its logistics) industry. If the device became affordable then that would address equality and food poverty aspects too. Just a thought 
A Circular Food Cycle
This diagram shows the more complex scenario associated with the typical food cycle today. Transport may take place between most steps, and some of that might be on a global scale - adding to costs and environmental impact.
[By the way the diagram at the top of this page doesn’t reference resource consumption and pollution. An important factor in food production, as it includes water and climate issues.]
The diagram illustrates the steps that could be removed if innovations allowed households and local communities to have full control and scope over the entire cycle, rather than relying on distant suppliers. Removable steps being: harvest, process, packaging and transport. (This assumes an innovation that allows an household, or local business, to grow food on demand.)
Similarly, if policies supported local small businesses then this could provide a sustainable, and fairer, local economy. Innovations might also be adopted that allow any locality in the world to produce any type of food product, not just those that are native to the area.