There is an inch and a half brown caterpillar thriving on the basil plant. What will this caterpillar become?

That depends on the mood you are in. If you are in a good mood, you will leave it alone (or relocate it) and one day, it will be a butterfly. But given that caterpillars love to eat the leaves of plants (especially basil) and destoy them, some people are not in a good mood when they see these insects, and they either kill them with pesticides or find natural ways to drive them out.