How we can mine asteroids for space food

Easy

Set first a logistically optimal delivery infrastructure to low earth orbit/Geo with reusable rockets

Use said rockets to set up an advance lunar post with Kickstarter key infrastructure delivered to develop the post into a full starter colony

Use the colony infraestructure to develop orbital rails, able to deliver orbital mass.

Deliver multiple prefab modules, able to be joined, into low earth orbit

Set up several space stations as refueling, tourist, and research areas. Use these to prop and kickstart your economy

At the same time, automate the colony creation process to create mining modules and set up shop near known asteroid belt targets with an advance team.

Optimal: prop up several refueling stations on the way

Standardize the mining process. Set up a loop of barges/pods going and coming from/to the target mining post to the moon surface or to the research stations

Escalate as necessary

You can't even mine an asteroid. End of that conversation right there.