I'll admit I don't use herb stems. I have a hard time using up all of the herbs that I do buy from time to time! For me, this means excellent planning of dishes throughout a couple weeks that use the same herbs. The only time all of this makes sense to me is when my herb garden on the window sill is healthy and thriving. Then, I pick from the basil, dill, thyme, parsley and cilantro plants as I need them.
Alex Delany of Bon Appetit, though, says that, based on the recipes we use, we've been conditioned to think that anything on the herb plant other than the leaves are compost (and, if you're not composting, you're trashing it). Yet, while the flavor of the stems of soft herbs (not woody herbs such as rosemary or oregano) might not be quite as pronounced, it's still very much there. They may not be great for sprinkling or garnishing but the can boost salads, soups and pastas to new heights.
Pesto and Salsa Verde
A case in point is pesto. Any part of the basil herb with olive oil, garlic and pine nuts will puree into a perfect pesto sauce. The same can be said for salsa verde. If you're using a blender, throw the stems in.
Broths and Soups
When building a quick broth, there is so much you can do in the flavor-building category. Parmesan rinds, miso, and alliums like garlic and onions are all great. Herb stems belong in that pot, too. They'll lend an herby depth to your finished product, and since you're straining the stuff anyways, you don't even have to chop them up — just toss them in and simmer away. You can, also, chop them finely and stir them into pretty much any soup right at the end of cooking to add a pop of brightness and texture.
Salads and Vinaigrettes
Incorporating finely chopped stems into your salad — whether it's a simple green salad or a more elaborate, veggie-packed situation — adds herby complexity. Also, you can also chop them up and stir them into the vinaigrette dressing.
Clearly, since I do use herbs, I do need to think differently about them.