The "big burst" problem is usually solved by a few (say 4) plants, not one.

But another thing about growing anything is that it works better if you work around it's schedule rather than the other way around. Hothousing and international shipping have got us out of the habit of thinking seasonally or by growth cycle of a plant, but it's not hard to adapt to.

Also for a lot of our food stuffs, they exist specifically to deal with an excess you can't deal with at the time of harvest. Things like tomato sauce, various jams, etc. All of that is designed to take a bounty of a crop, and turn it into a form you can eat in the middle of winter when everything is dead outside. Today though, we think nothing of the implications of this as we buy a jar of ragu once a week.

Add 2 more basil plants and prune 1/3 the leaves when you use it.

Pruning the basil will also cause it to grow bigger and better

Easy. Grow more basil. Eat more basil regularly. Make pesto with excess basil. Freeze basil. Life gave you lemons, so make lemonade.