1. Freeze it
I have an ice cube tray specifically for basil so my normal ice does not taste like basil. Pack as much washed and cut basil as you can into the cubes. Fill the rest of the way with water and freeze. As soon as the cubes are frozen, empty into a freezer safe bag. You can just throw these cubes into anything you want, or melt them in a bowl and take the basil out if you don't want the water.
2. Make Basil Butter
One of my favorite things to do with Basil. You can use this for sauce over pasta, on bread then broiled, served with rolls, in sauces with veggies, or on meats. I usually make a lot when I do this because it's just as easy to make a ton, and you only have to wash up once.
3c basil 4 cloves garlic
1lb butter Fresh ground pepper
Throw it all in the food processor and blend until smooth. Transfer to an airtight container or make balls with a small ice cream scoop. Put balls on a cookie sheet and place in the freezer. Once frozen transfer to a freezer bag and freeze to use all winter! Not only are they delicious, but they are pretty too!
3. Grow more
I have not tried this yet, but it worked for my mom! Put a sprig of basil in water on a windowsill and it will grow roots. This way you can have a small plant in the house all winter. I think I will try it, even though it will be hard not to use it all at once!