Heat 2 tablespoons oil in a large pot over medium-high heat. Add pork; cook until browned, about 2 minutes per side. Pour in 2 cups chicken stock. Reduce heat to low, cover, and simmer pork until is fork-tender, about 1 hour. Shred with a fork and transfer to a plate.
Heat remaining 1 tablespoon oil in the pot over medium heat. Add pigeon peas and onion; cook and stir for 2 minutes. Stir in arborio rice. Pour in enough chicken stock to barely cover the rice; cook and stir until absorbed. Continue adding stock, stirring often, until each addition is absorbed and rice is tender yet firm to the bite, about 20 minutes.
Fold shredded pork into the rice. Sprinkle Parmesan cheese on top.