Heat oil in a medium saucepan over medium heat. Cook onion, celery, and carrot until translucent, 6 to 8 minutes. Add potatoes and white beans and cover with water by 2 inches. Season generously with salt. Bring to a boil, then reduce heat and simmer until potatoes are tender, about 8 minutes. Drain, reserving about 1 cup cooking water.
Mash vegetables, adding reserved water to adjust consistency. Season with salt and pepper and drizzle with oil before serving.