Is this basil root rot?
Thank you for choosing Ask an Expert for help with your winter basil problems. Root rots/problems of any kind generally result in yellowing, wilting leaves as water and nutrients are unable to get to the top of the plant. Your plants would appear to be doing well, if the tops are in good shape.
High humidity in the container or the soil holding too much water can encourage a disease organism. Crowded plantings, especially indoors, are prone to these conditions, so be aware to prevent any disease from starting up.
I cannot tell how old the plants are, but if the leaves of the plant continue to be healthy, it may be that the plant is maturing and forming a woody base (which is natural).
Check out the Oregon Extension publication Growing Your Own (see here: https://catalog.extension.oregonstate.edu/em9027) It includes information on all kinds of home gardening - both in-ground and in containers.