It’s up to you. Some gardeners pull the whole plant and hang it upside down in a basement or garage, while others just harvest the ripening peppers. The fruit can be placed in a paper bag with an apple to help hasten ripening, if you prefer. If you have lots of peppers that are not up to full size yet, you might try pulling the whole plant in case the plant can still give the fruit a tiny bit more nutrients before the plant dries. But if your peppers are mostly of a mature size, then just harvesting the peppers themselves should work fine.
It’s up to you. Some gardeners pull the whole plant and hang it upside down in a basement or garage, while others just harvest the ripening peppers. The fruit can be placed in a paper bag with an apple to help hasten ripening, if you prefer. If you have lots of peppers that are not up to full size yet, you might try pulling the whole plant in case the plant can still give the fruit a tiny bit more nutrients before the plant dries. But if your peppers are mostly of a mature size, then just harvesting the peppers themselves should work fine.