Several herbicides that would kill it are 2,4-D and glyphosate, and fall is a good time to spray it, but these herbicides will kill your good stuff. Plowing or putting that field into grain for a season are options, but if it were mine I might try imazethapyr 2sl, although wild carrots aren't on the label this stuff is potent on things in the carrot family.
Spot spraying it is a good option if the area is small. Mowing low and often to keep it from seeding would be another option.
In deer plots if I have plenty of acreage I sometimes just ignore weeds like this for a while and eventually switch the field to a burndown followed by rye to clean everything up at one time, because rye suppresses grasses and can be spread with 2 4-D, followed by a new clover seeding.
In limited acreage situations I'd do the spot spray route.