So, when my basil gets this large, my go to technique is pesto. Now pesto actually just means a paste of something, and pesto can be made from lots of herbs - tarragon, cilantro, parsley, arugula - as well as other things like nuts.
A traditional basil pesto contains Parmigiano Reggiano cheese. Not Parmesan that you buy in the US, not the stuff in the green shaker, but the real thing, which you know from the stamped label on the rind. It comes from the Emilia Romagna region of Italy, known as the epicenter of great food in Italy. By the way, don't throw that rind away - they sell them for about $7 a pound at Whole Foods, so put them in a bag and freeze them for flavoring soups and stews later. When I make pesto to freeze, I leave the cheese out. That way I have flexibility for using it in a citrus pesto without the cheese if I choose or adding the cheese when I later thaw it. Adding cheese at this point also just increases the volume, and I don't want to take up more freezer space than I need to.
And one of the best ways to freeze pesto (basil or otherwise) is to spoon it into an ice cube tray. Once the cubes have frozen you can just pop them out into a bag or other covered container. The individual cubes seem to be just enough pesto for a recipe for two and you then aren't continually thawing and refreezing the remaining pesto. So take a few minutes this week to make some herb pesto - either with herbs from your own garden or from the bountiful stock at the farmers' markets. Around the end of February you'll be really glad you did!