Heat olive oil in a soup pot or dutch oven over medium-high heat.
Add the onion, bell pepper, carrot, garlic, jalapeno and a pinch of salt and pepper. Saute until tender, 5-7 minutes.
Add in the diced ham and saute 2 more minutes.
Add the black-eyed peas, broth, chili powder, cumin, and bay leaf to the pot. Stir to combine then bring to a boil. Reduce heat to low (or a light simmer) and let simmer, covered, until the peas are very tender, about 1 1/2 hours.
When the peas are tender, add in the kale and stir in until wilted down into the soup. Taste the soup and add salt and pepper, if desired (this will depend on how salty your ham is).
Remove the bay leaf. Serve and enjoy!