In a large heavy pot, heat the oil over medium high heat until hot. Stir in the onions, garlic, and 3/4 teaspoon salt and cook, stirring occasionally, until golden, 6 to 8 minutes. Peel and dice the potatoes. Stir in the stock and potatoes, then bring to a gentle boil. Cook, stirring occasionally, until the potatoes are very soft and starting to fall apart, 45 minutes to 1 hour. Stir in the arugula until just wilted, about 3 minutes, then season the soup with salt to taste and serve.