Cook pepperoni in a deep 12-inch 5-quart saute pan over medium heat for 2 to 3 minutes until its edges curl. Transfer to a plate, leaving 1 teaspoon rendered fat in the pan.
Add beef and onion and brown over medium-high heat for 8 minutes, breaking up the meat and cooking to 160°F. Drain excess fat and stir in garlic and oregano for 30 seconds.
Add tomato sauce, broth, ditalini and salt. Simmer uncovered over medium-low heat for 10 to 13 minutes, stirring every 2 minutes and adding reserved water only if needed before pasta becomes tender.
Stir in olives and half the pepperoni. Scatter mozzarella and remaining pepperoni over the top.
Cover and heat on low for 3 minutes until cheese melts, then rest off the heat for 2 minutes before serving.