It's hard to ID the damage if an insect isn't present and visible, although a type of caterpillar, grasshopper or cricket, slug/snail, or beetle can all create similar-looking damage. The remedy for reach of those culprits would differ, so until it should be identified before any treatment is attempted. You can inspect the plants (especially the leaf undersides) during the day and after dark in case it's an organism that only feeds at night. A physical barrier like row cover or insect mesh netting can help to exclude pests, but only if it's put over plants before a pest arrives, and it such measures would not help with slugs/snails. (Row cover also helps to insulate early-season crops, and basil is not fond of chilly temperatures below about 50 degrees (45 degrees at a minimum). Cool soil temps can also stagnate growth, so could slow the plant's ability to grow new leaves.)

For now, see if you can catch the pest in action, and just keep an eye on the plant's watering needs since basil does not like drying out and our weather is still quite dry overall (and the rain deficit has been worsening).

Miri