Place potatoes in cold salted water and bring up to a boil, simmer 1 minute. Remove with a slotted spoon. Add beans to water and simmer for 3 minutes. Remove with slotted spoon.
In a saute pan over medium-high heat, heat 1/3-cup extra-virgin olive oil. When oil is hot add potatoes and cook for 8 minutes until light brown. Add garlic and season with salt and pepper. When garlic is light brown, add the chili flakes and saute for 10 seconds, then add oregano. Continue to saute for 4 minutes. Using your hands, squeeze the tomatoes between your fingers right into the pan. Add 1 cup cold water. Add broad beans. When it comes to a simmer, reduce heat to low and simmer for 10 minutes. Turn off and let sit 5 minutes, then stir in remaining olive oil. Taste and adjust seasoning, if needed, and serve immediately.