It's probably a trait that's findable in most perennial species, just rare. I know Mark Shepard plants nut seeds all over his property, and sometimes finds nut trees that produce nuts in their first year. (He tends to save those seeds and plant them in hopes of getting more trees like that, of course.)
As for wild plants, I'm not sure how many set seeds in their first year consistently. Most plants I know are are domesticated, or semi-domesticated. Here's what I can think of off the top of my head.
- Some wild banana species, especially short ones that are adapted to temperate climates. (Yes, those exist! I'm collecting those seeds because I'm planning to cross them to try to get a temperate-friendly landrace going.

)
- Tomatoes, of course, and peppers, and plenty of other nightshades, like Solanum habrochaites.
- Fig-leaf gourd.
- Chayote. (Although chayote is weird -- it's viviparous, so its whole fruit is the seed!)
- Sweet potato.
- Stevia.
- Basil.
- Echinecea.
- Runner beans.
- Dandelions.
I'm sure there are loads more.
By the way, I suspect a lot of what we call "biennials" are actually winter annuals -- they complete their whole life cycle within one year and die after making seeds once. There just happens to be a winter in the middle of their life cycle.