In 5-qt saucepan, heat oil over medium-high heat. Add onion. Stir occasionally until tender.
Add garlic and red pepper. Stir occasionally until garlic is fragrant, about 3 minutes.
Add stock, potatoes, and salt. Bring to a boil. Turn down heat and simmer for 10 minutes, until potatoes are tender enough to pierce with a fork.
Add green beans and cover. Simmer for another 6 minutes. Once green beans are tender and bright, remove potatoes and beans from the liquid with a slotted spoon and put into a serving dish.
Return pot to heat and bring the remaining liquid to a boil. Let it reduce until 1 cup remains. Spoon liquid over veggies to serve.