This is a classic French recipe. It has a nice alliteration and both the pigeon and peas have the same seasonality.
But the classical recipes call for about one and a half hours of cooking, which turns the peas into mush and the pigeon becomes tough. It also uses thick slices of bacon.
So, I changed the order of things a bit.
Firstly, I cut the pigeon in two and cooked it in butter and when it was browned, I added water (or wine or another liquid) and kept cooking for half an hour so that the pigeons were ready.
Then I cooked the shelled peas for 5 minutes in water, with a “bouquet garnie” of dried herbs, salt and pepper and I added some cut-up chorizo and the pigeons and continued for five minutes.
I took the pigeons out, discarded the herbs, drained the peas and served it together