Oregano and peas seem like a bad match. The musty, pungent herb and the fresh, bright legume would seem to fight. Maybe this hunch stems as well from their divergent seasons, the spring of the peas, the summer of oregano.
But when concocting a chicken and peas dish for dinner recently, I had no fresh herbs in the house except slightly wilting oregano left over from some now-forgotten recipe. I wanted that extra element an aromatic herb would provide, so I said to heck with it, chopped a bunch of the leaves finely and threw them in. The combo was a revelation. Oregano does go with peas, and brings together the chicken, mushrooms and onions nicely.
I would recommend that using fresh oregano is vital here, but maybe I would be wrong about that too.