Put the peas in a large pot with the chicken broth.
Boil till peas are tender. This might take 1/2 hour or 2 or 3 hours depending on the peas, whether you soaked them, and your altitude. (It takes longer in mile-high Albuquerque). Add water if liquid is reduced too much. It's fine for them to be quite soupy. (I tried cooking in a pressure cooker, but the vent got clogged up and I'm lucky the cooker didn't blow.)
In a skillet, saute the onions and carrots in oil till carrots are just starting to get tender.
Add the garlic to the skillet and cook a few minutes more.
Add the spinach to the skillet and cook till it is wilted. Just a minute or two. If you use kale, it will take a little longer.
To the peas, stir in the tomatoes, salt, pepper, and the onion/carrot mixture.
Add more broth or water if you want it to be soupier.
Bring everything to a boil.
Taste and add more salt/pepper if desired.