Probably more humid than you might realize next to the window. The plant doesn't look like a begonia because the leaves don't look 'lop sided' (a/k/a asymmetric) as all begonias do. It looks nice and healthy, you must have good luck with plants.What is the plant with the white flowers?

I agree with Woebegonia. It doesn't look like a begonia. Probably a weed seed lodged there and germinated when the weather warmed up. Blooms should help ID it for sure. Photograph the plant at different angles and close up for more detail.

PS if it was a begonia more than likely it could come from seed as the wax type begonias often spread seed far and wide which will survive winter.

Here is an example of one from last year alone. Typically I see these in my pots instead of cracks in the flagstone.

the white flower is lobelia.