The phrase "tough stalks" refers to the strong and resistant parts of plants, such as stems or branches, that are difficult to break or chew. Full definition
Remove tough stalks from the parsley and chop roughly. (nourisheveryday.com)
It's not as labor intensive as shelling peas but for salads, I trim away the tougher stalks, using only the tips and tendrils. (mixedgreensblog.com)
The best way to deal with this is to pick out and discard any damaged or brown leaves and remove any tough stalks, fill the sink with cold water, then plunge the spinach in the water and swirl the leaves around. (deliaonline.com)