In a large Dutch oven or heavy pot, cook the chopped bacon over medium heat until browned and crispy. Use a slotted spoon to remove the bacon and set it aside on a paper towel, leaving the rendered fat in the pot.
Add the diced onion to the bacon fat and sauté for 4–5 minutes until softened. Add the garlic and cook for another 60 seconds until fragrant.
Add the trimmed green beans to the pot and stir to coat them thoroughly in the fat.
Add the potatoes, chicken broth, pepper, and sugar. The liquid should just barely cover the beans and potatoes.
Bring the mixture to a boil, then reduce the heat to low. Cover with a tight-fitting lid.
Simmer for 45–55 minutes, or until the beans are very tender and the potatoes are fork-tender.
Stir the cooked bacon back into the pot. Taste and add salt if needed. Serve warm with plenty of the cooking liquid.