It’s probably not exotic for folks across the pond, but I grow chillis every year with some success, as long as I can get them germinating on a windowsill (we have no greenhouse) by mid February, then the growing season is long enough for them to ripen. In successful years ( like this one), we still have fresh chillis at Christmas.
If you are thinking about asparagus, two things from experience. Don’t bother unless the bed you are planting it in drains really well. Secondly, once they grow the spears grow really fast and can go from perfect to eat to hard and woody in days. So because our allotment is far enough away that we only go up once a week, we often missed out on the perfect spears. Have now replanted the asparagus be with chard, although the odd spear still pokes through.