Hi, and welcome to ATP!
It will be much easier to ID if/when it blooms if you are patient enough to keep it alive that long. Is the second picture about the size of the whole plant? The single leaf reminds me of Calendula, but they really don't like hot weather, and would have bloomed by now with distinctive yellow or orange-y daisy like flowers.
How tall is/was the entire plant? Are the lower stems woody or green? Do the leaves have any scent? (rub between your fingers and sniff) Did you start the basil plants from seed or buy them? Were the plants outside where a bird could have dropped a seed into the pot?
