You can boil the potatoes and steam the beans at the same time. Start with the potatoes: put them in a large pot and cover with cold water. Add 1 tablespoon salt and bring to a boil. Reduce the heat and simmer, uncovered, until the potatoes are tender when you stick a fork in them, about 30 minutes. At the same time, combine the cream and butter in a small saucepan and warm over low heat until the butter is melted. Remove from the heat and cover to keep warm.
While the potatoes are cooking, start on the beans. Break the beans in half and put them in a colander large enough to fit over the pot the potatoes are cooking in; set aside. Now heat a large saucepan over medium heat. Drizzle 2 tablespoons of olive oil, add the bacon and cook until the fat is rendered, about 5 minutes. Add the onion and cook, stirring, until softened, about 3 minutes. Add the tomatoes to the pan, crushing them in your hand as you do so, to break them up. Stir in the sugar. Bring to a boil, reduce the heat and simmer, uncovered, until thickened, 7 to 8 minutes. Remove from the heat.
When the potatoes have cooked about 20 minutes, put the colander over the pot and cover the whole thing with aluminum foil. Continue cooking until the beans are crisp-tender, 5 to 7 minutes. Remove the colander from pot and dump the beans into the pan with the tomato sauce; fold in the beans and season with salt and pepper.
Now drain the potatoes in the same colander and dump them back into the pot. While the potatoes are still hot, pour in the warm cream and butter and mash the potatoes with a potato masher. Season with salt and pepper.