Here is a very simple way to use a whole bunch of basil, and the result has multiple uses. It is good on pasta or mashed potatoes, or to dress up a soup. Fold a little into some mayonnaise or aioli to use as a sandwich spread or to top grilled fish. Or, try working a bit of pesto into a vinaigrette for a different flavor.
Combine the basil, garlic, cheese, salt, and pepper in a blender or food processor and process briefly. With the motor running, add 1/2 cup oil in a slow, thin stream. Continue processing until the pesto is the texture you prefer. If you plan on keeping this for a while in the refrigerator, float a tablespoon or so of oil across the surface to keep the top from turning dark, then cap tightly. It should keep until it’s all used up. Serve at room temperature.