Heat 1 tablespoon oil in 5-quart Dutch oven over medium. Stir panko 2 to 3 minutes until golden. Transfer to dry plate; cool slightly and mix with 2 tablespoons Parmesan.
Add remaining oil to same pot; raise to medium-high. Season chicken with salt and pepper; cook 4 minutes, stirring occasionally.
Add garlic and oregano 30 seconds. Add sauce and broth; scrape bottom and boil.
Add rotini; simmer uncovered 12 to 15 minutes, stirring often, until pasta tender and chicken 165°F. Add reserved water if sauce dries before done.
Remove from heat; fold in remaining Parmesan. Scatter mozzarella; cover and rest 3 minutes until melted.
Divide among 5 bowls; scatter breadcrumb mixture over just before serving.