Heat oil in a small saucepan over medium. Cook garlic 30 seconds; add tomatoes, oregano, salt, and pepper. Simmer 10 to 12 minutes until thick, stirring frequently.
Heat broiler. Toast bagel halves cut-side up on a sheet 1 to 2 minutes until pale gold.
Spread sauce evenly on four bottom halves, leaving a small border. Add pepperoni and half the mozzarella.
Divide remaining mozzarella among four top halves. Broil all halves cut-side up 2 to 3 minutes, watching constantly, until cheese melts and browns in spots.
Use a spatula to turn cheese-covered tops onto filled bottoms. Rest 2 minutes; halve and serve while cheese is soft.