This will require some of the skills discussed in the post from Jan 6th. Be aware that working with glass is hazardous. A wrong move could lead to losing a finger or an eye, so proceed at your own risk. Also note that professional car mirrors are made of tempered glass, which shatters to tiny pieces when hit. This is considered safer in case of accidents, as regular glass can break into knife-like shards that are very dangerous when flying around. It's hard to find tempered mirror glass, and it's very hard to work using the following methods. If you decide to use regular mirror glass, be aware that it's riskier, and might be against the law in some states and countries.
1. At Home Depot or Lowe's, get a piece of mirror. You might be able to find a piece of tempered mirror, but be aware that those are hard to work. Also, get some two-sided thick tape. Be sure that's good quality tape, so the new mirror won't fall off in the 1st curve. You will also need a glass-cutting kit, a sharpie, a metal ruler and a pair of pliers.
2. Tape a piece of clear plastic to the original mirror, and draw-out the shape of the mirror using a sharpie. A sharpie is usually thick, so take note which side of the trace is the "actual" shape (mostly, we would draw from inside the frame, making the out line "count").
3. Cut the plastic around the shape using scissors.
4. Tape that to the uncut mirror, and re-trace the shape on the mirror using the sharpie.
5. Using standard glass-cutting method cut the mirror to a shape approximating the right shape, leaving off the corners.
6. Using the pliers, chip-off little pieces of the glass, thus gnawing it to the right shape. It doesn't have to be ultra-precise - just as long as it fits in the frame. A normal mirror can be chipped-down in about 10 minutes. It might take a few attempts until you get it to match perfectly.
7. Using the double-sided tape, glue the mirror into place. It can be glued directly on a previous sheet of glass, or the old glass can be shattered and remove, and then glued on the frame. 8. for advanced and experienced users: You can also do this using a wide-angle panoramic mirror, which are even more expensive. This, however, is much trickier as their uneven surface makes them very hard to cut straight. My recommendation is to use the chipping method to skip step 5 and shape the glass complete using the pliers. It's time consuming, and not without risk, but may be worth the time.