Heat the oil large stock pot over medium-high heat.
Dice the country ham into bite-sized pieces. Once the pot is hot, add the country ham and sauté for 2-3 minutes until the ham is light pink and starting to brown on the edges.
Add the onion. Sauté until the onion is translucent, about 8-10 minutes.
Add the minced garlic and sauté for an additional 30 seconds.
Add the green beans and potatoes to the pot.
Pour the chicken broth over the top of the vegetables.
Add the Cajun seasoning, ground black pepper and red pepper flakes. Add salt to taste.
Bring the pot to a boil, then cover it with a lid, reduce the heat to medium-low and cook for 30 minutes. The green beans and potatoes should be fork tender when they’re done.
Remove the pot from the heat and allow the beans and potatoes to sit for at least 15 minutes. The vegetables will continue to absorb the flavors of the ham and the broth as they sit.
Season with additional salt and pepper if necessary.