The flowers look a lot like the white flowered form of Dame's rocket, Hesperis matronalis, but the leaves look a bit off. I know they can be variable in shape, but those look overly large.

Looks like wild mustard....?

All the mustards I know have yellow flowers. But definitely a Brassica. Certainly looks like a bolted Vegetable to me. Is that a bird feeder hanging there? Could be the source of your mystery plant?

I think you all are right that it is a brassica. The closest I have found to it is Brassica juncea but even it isn't an exact match. The veins in the leaves of mine are darker than the photos I found online, plus there is the white flower vs yellow. btw, the wrought iron thing above it is a candle holder.

Money Plant?

Might it be a bolting radish? Lower leaves look very radish-like...?

The leaves certainly look just like bolted radish leaves but the usual little red radishes have flowers which are looser and pinker. However, daikon radish, which I have never grown, appears to have white flowers similar to th OP's plant. The leaves aren't right for Money Plant (Lunaria).

I'll give it a bit longer and then pull it up to see what the roots look like. I tasted some of the flower buds and they didn't have much of a taste. It does look a lot like radish leaves, but the plant is way too tall, at least compared to the radishes I've grown before.

Have you had radishes bolt? The flower stem can get a couple of feet tall and if this is Daikon it could well be that big.

Hesperis produces narrow, pointed, undivided leaves and longer, narrower flower spikes.