Preheat a large nonstick skillet over medium-high heat and brush with the canola oil. Fry the pepperoni on both sides until curled, then remove from the skillet. Portion the ground beef into 4 hamburger patties and sprinkle with some salt and pepper. Cook the burgers in the skillet to the desired doneness. Remove to a plate and tent with foil to rest. Wipe out the skillet and return to the heat.
Place the bagels in the skillet cut-side down to toast until golden brown, 3 to 5 minutes. Reduce the heat to low. Flip the bagels over and spread marinara sauce across each, then top them with cheese. Cover the pan and cook until the cheese begins to melt.
Sandwich burgers and pepperoni between pizza bagels and serve.