In a large heavy-bottomed pot or Dutch oven, sear the beef chuck pieces over medium-high heat until completely browned on all sides. Remove the beef and set aside.
Return the browned beef to the pot. Stir in the rinsed split peas, black pepper, and beef broth. Bring the mixture to a rolling boil.
Reduce the heat to low, cover the pot, and let the soup simmer for 60 to 75 minutes. Stir occasionally until the split peas have broken down and the beef is very tender.
Remove the pot from the heat. Gently stir in the heavy cream and freshly chopped mint.