A traditional glass mirror won't work. Among other things, the heat will eventually damage the silvering on the back of the glass. The glass itself also risks breakage from the heat.

A few companies offer polished stainless steel reflectors, but if that is your fireplace in the photos above, I don't think any of the "off-the-shelf" sizes are going to work.

It is possible to have a company custom make stainless steel panels, but something that large will be difficult to keep flat with the expansion and contraction associated with the heat.

Another possibility, which will give you some reflection without being a mirror, is a black porcelain back, like in this fireplace:

Thanks for the great advice. Is the black porcelain back individual tiles or a single sheet item custom?

A single panel. I'm not sure who could make a custom one.

One other thought occurred to me after making the comment above that would probably be more economical (but not cheap) from a custom standpoint.

You could have a single piece of ceramic glass made and back-paint it black with high temperature paint. That would be simpler than having a custom porcelainized piece made. Ceramic glass is designed to handle much higher temperatures. The reflection on the inside of the ceramic glass is what is creating the "infinity mirror" effect on the fireplace above.

beautiful fireplace, if you go for a custom stainless steel, you will want to use 10 ga or higher so it will be less likely to warp from the heat. The thinner material will warp quicker. It will also depend on how long and often you use the fireplace.

that backslash really catches your eye, complimented nicely with the cabinets