I cook Italian, so tend to use both Basil and Rosemary on an almost daily basis.
Have been experimenting for a while with attempt to grow harvestable supply all year round of both herbs.
Rosemary survives outside in winter, but does not thrive, and will be some months before it is sufficiently productive to cut. Indoor-grown did not do well. Pots which I put out in Winter, and let them experience cold, but I bring in to save them from most severe freezing are doing best.
Basil died, it did not survive my attempt to grow indoors over Winter. (outdoors, only crops in Summer)
There are a lot of variables, so I will keep on trying. Commercial herb farms do grow them over winter, but they have computerised climate control to help get it right.
In past, have grown a lot of lavender: probably main scent of my garden and home. But it had spread to take up too much room. I needed the space, so have grubbed it out. Have kept a handful of rooted cuttings, so can re-establish a smaller lavender patch to attract bees.