If you want to root larger branches of your Laurus nobilis, then I advice not to cut the branch off until it is rooted.
Dependent of the shape of your shrub I would, if possible, fix one of the lowest branches into the soil and make sure a piece of at least 5 inches are covered with a couple of inches of soil. If you do it now, then expect new roots next spring on the covered piece. Then you can cut the branch off to form a new shrub. Check the size and condition of the new roots before you cut. For some evergreens the methods works best if you start in the early spring.
This method is called layering.
If no low branches can be covered with soil, then consider the root ball method. You then takes the soil to a branch using a plastic bag.
Follow the guide in the linked video. Watch how some parts of the bark are removed. This trick is useful for the first method too.