Food Delevery LLC?

There may be some legal benefits, but from a tax standpoint if you are the only owner of the LLC it would be treated the same way - as your LLC would be known as a "disregarded entity."

For tax purposes, your vehicle is already a "company vehicle" and your miles are already business miles. 

Be sure that you are keeping track of the miles you are driving while delivering as well as all of your other business expenses for your taxes next year. Everything that you spend money on for the business of delivering food has the potential to lower your tax bill next year - bags, supplies, miles, car washes, uniforms, name tags, advertisements, etc.

You may want to take a look at this article for some great tips: Top Tax Write-offs for the Self-Employed.