I am growing pole beans on the outside of the pea pen -- the bean plants are trimmed off by the birds wherever they can reach them through the fence, and they adore the green and yellow beans too
(I planted the pole beans as a treat for the birds and to help reduce boredom, so the whole point is for the bean plants to get eaten...) I would grow peas for the Peas the same way, but it is too hot here in the summer, and too cold in the winter, and too brief in the spring
But I am absolutely certain my Peas would love peas, especially the whole plant!
I have a large planter full of Swiss chard, which has been a huge hit. They get all the ratty and overgrown leaves, and they love it. (There's a lot of ratty leaves -- I finally discovered one of the dogs is trying to eat the chard.) It's a nutritional powerhouse, so I'm glad to share it with the peas. They love squashed cherry tomatoes.
I give the birds all the seeds from cantaloupes (along with some of the fruit), but I tend not to give them the rinds, unless I cut up small bits. I worry about choking as they gulp stuff down pretty fast, and cantaloupe rind is pretty tough. Same with other melons, like honeydews.
I've given them homegrown sprouts, and I just went last week and got some new, different kinds of sprout seeds to try. I've seen pictures of sprouting bins that folks have set up to grow and treat their chickens, and I think the peas would really like that if I got it going. I would not give large quantities of fresh, first growth alfalfa though, and don't plan to give large quantities of alfalfa sprouts, because I worry about the level of nitrogen. I think a little bit would be okay, but I'm not an expert on this.
I am not putting any of the vegetation from any of the solonacea family of plants into the pen -- no leaves or stems of tomatoes, peppers, potatoes or eggplant -- and no rhubarb. They are leaving the tomato plants that overgrew the pen mostly alone (it is reportedly poisonous, although I do not know how toxic it actually is) -- but I probably won't plant tomatoes quite so close to the pen next year. I'm glad they are not devouring it, for sure, or I'd feel like I needed to pull up the plants.
Oh, did I mention they are crazy for strawberries? But who isn't?
(In this house, unfortunately, all the strawberries come from the store...) The birds get the strawberry caps and some fruit. Also peach peels and apple peels, carrot peels (but I don't give them the chunky cut off ends unless they are diced up so they can't choke), and other fruit trimmings. I don't give potato peels (Solonacea again), and I don't give any onions or garlic, as I am concerned those could be toxic. Salad greens, yes, for sure I give them those, you betcha. The birds are trimming off any pumpkin tendrils and/or leaves that grow into the pen, ditto the watermelon plants, and I think those are all safe.
Who knows, maybe I worry too much about the birds choking?
But my birds are penned, not free ranging, so it's an artificial, confined environment to start with. There's other birds competing with them for the handouts, so they get pretty grabby and gobble stuff pretty fast just to beat out the other birds for the treats. It's not a bird wandering loose, with all day to decide whether to try to swallow something, it's the whole group, everyone trying to grab something first. So I worry that in that situation, they might accidentally try to swallow something that could choke them (like a big, unsquashed, too tough cherry tomato), without having had time to consider it, or tear it smaller, and then what would happen? I am so not ready to try the Heimlich maneuver on a panicking pea
If something is hard or tough, I try to make sure it is in a shape that won't block an airway.
I think edible flowers (think roses and squash blossoms) would be okay, but I would not plant a rose bush next to the pea pen, because of the chemicals that occasionally are required to treat the rose bushes. I bet lavender would be okay, but I would research it to double check before I planted it next to the pen.
Oh, and I almost forgot, boy do the peas ever love corn on the cob!
The cobs are too big to swallow, and it's a definite boredom-buster. They will chase the cobs around for quite awhile, getting after the bits of corn. Of course, they also love bread and scratch grains, so we have totally solved the stale bread problem at my house
But I don't give very much bread, and I don't give it very often, because I don't think it's all that healthy, so it's an occasional treat.
Hope this helps