Can't comment about "Pesto perpetuo." But any sweet basil would be hard pressed to survive on a window sill for the winter. Sweet basil is an annual - 1 growing season lifespan. Some can keep them going long but their vigor is spent and they are a shadow of their former self. Plus meager winter sun through a window is not the light a basil requires. They grow in full sun. Enjoy your basil now. Bring it in if you wish, but don't expect it to be in next year's garden.

FataMorgana

perpetuo is a variegated variety that can be grown as a perennial in zones 9 and up. With sufficient light it is supposed to be able to live in doors. The reason that this is possible is because it is a non-flowering variety, so it doesn't bolt. I guess my question was if anyone else had this "non-flowering" basil produce flowers.

Mine flowered too!

You might have a chance with a grow light but the truth is that most herbs want to live outdoors in sunlight and sulk or die under indoor conditions. Often, variegated plants have a tougher time surviving, indoors or out, because they have less chlorophyll.

I know this is a bit late, but I just came across your post because I also have a flowering Pesto Perpetuo. It’s been living in my window all fall and winter, and it’s doing great. I’m not sure how it could have cross-pollinated with another basil plant since it doesn't produce flowers, but I’m excited to see if it will produce seeds!

Mine also flowered! It's in my raised outdoor bed and has survived and thriving with one of the hottest Texas summers on record with over 23 days of highs being 100-110!