Q.Why Is The Stem Of My Angel Wing Begonia Turning Brown. The Rest Of The Plant Is Very Healthy With Tons Of New Growth.
My plant is a cutting from a larger plant and I’ve been growing the cutting about a year and a half. It’s shot another plant out of the soil and both stems from the soil are about three feet tall. Lots of leaves and flowers. I noticed the stem of the original cutting is browning. But tons of new growth on that stem and the other. New flowers and three new leave on that stem alone.

Certified GKH Gardening Expert
Older stems on cane begonias get woody and can be removed when you prune each spring. If the spots are not soft, I wouldn't be worried. If they are soft then stem rot might be growing, but it doesn't sound like it since you are getting lots of new growth.
This info may be helpful:
https://www.begonias.org/cane-like-begonias-like-bamboo-with-flowers/