Like the Ant said to the Grasshopper:
You should make pesto in the summer, but don't just make enough for summer - an afternoon spent freezing pesto in the summer will pay you back a thousandfold in the happiness you will get from eating lovely delicious homemade pesto in January and February when you are tired of root vegetables and nothing is growing yet.
How to make Pesto:
Pull 2 cups of fresh basil off the stems, and put them in a food processor with 1/2 cup of olive oil, 1/2 cup of parmesan cheese, 3 cloves of garlic, and 1/3 cup nuts. I use hazelnuts because that's what grows locally here in Oregon, but the most traditional thing is pine nuts. Walnuts will work well too. Process until it's all mixed and pretty smooth; you may have to do it in batches depending on how big your food processor is. Use immediately or freeze a cup at a time in tupperwares or plastic baggies. Label the baggies with the date so you'll know which ones to use first.
What do I do with pesto?
Most often I use pesto as a sauce for spaghetti, often with salmon or chickpeas and broccoli in it too. Sometimes I spread pesto on pizza instead of the tomato sauce. I also put some pesto in my tomato soup, to give it more flavor in the wintertime when fresh basil isn't available.
Vegetarian or vegan?
Naturally vegetarian. You can make vegan pesto by leaving out the cheese; some people like to double the nuts to make up for it, others don't.
How long will pesto keep?
You should freeze whatever you don't use immediately, so it will taste fresher when you defrost it. Frozen, it will last until next summer. To defrost it, either leave it on the counter for a few hours, or microwave it for a minute. Take it out of the tupperware before you microwave it, and put it in a microwave safe ceramic bowl.