Rinse the basil leaves and pat them dry before you start. Peel your garlic cloves and roughly chop them so they blend more easily. Measure out your mayo, yogurt, vinegar, salt, and pepper so everything is ready to go into the processor at once.
If you want a dressing you can pour over salad, add all the ingredients straight into your food processor. Blend until smooth, pausing to scrape down the sides if needed. This usually takes less than a minute of actual blending time.
For a dip-like texture, leave the mayo out of the food processor at first. Blend the basil, garlic, yogurt, vinegar, salt, and pepper until smooth, then transfer it to a bowl. Stir the mayo in by hand instead of blending it, which keeps the texture thick and scoopable.
Give the dressing a taste before serving it. If it feels a little flat, add a pinch more salt, a splash more vinegar, or a bit more garlic until it tastes right to you. Small adjustments make a big difference here.
You can use the dressing immediately, or pop it in the fridge for a bit if you prefer it colder. It keeps well in an airtight jar or container, so I usually make a batch ahead of time for the week.