In a large, deep skillet or Dutch oven, cook the diced bacon over medium heat until crispy. Use a slotted spoon to remove the bacon and set it aside on a paper towel-lined plate. Leave about 2-3 tablespoons of bacon fat in the pan.
Add the diced onion to the pan with the reserved bacon fat and sauté over medium heat until softened, about 3-4 minutes. Stir in the minced garlic and cook for an additional 30 seconds, until fragrant.
Add the green beans to the pan and toss to coat them in the bacon fat, onions, and garlic.
Pour in the chicken broth, then stir in the brown sugar, Cajun seasoning, Worcestershire sauce, salt, and pepper. Bring the mixture to a gentle boil, then reduce the heat to low.
Cover the pan with a lid and let the green beans simmer for 1 hour 30 minutes, stirring occasionally, until the liquid has reduced and the green beans are tender and flavorful. If the liquid reduces too quickly, add a splash of chicken broth as needed.
Once the green beans are tender and the liquid has thickened slightly, stir the crispy bacon back into the pan. Adjust seasoning with additional salt, pepper, or Cajun seasoning, if desired.
Serve warm as a side dish, and enjoy!