Line a plate with paper towels. Heat the oil in a large pot over medium-low heat. Add the bacon and sauté until crisp, about 4 minutes. Remove the bacon with a slotted spoon to the paper towels. Leave the fat in the pan.
Add the onions and stir for about 3 minutes until they start to turn golden. Add the garlic and stir for another 2 minutes, until the garlic turns golden. Add the greens to the pot and stir to coat them with the oil and onions. Cook, stirring, occasionally until they begin to wilt, about 5 minutes.
Pour in the broth. Add the red pepper flakes, season with salt and pepper, then turn the heat to medium-high and bring the broth to a simmer. When the broth is simmering, lower the heat to medium and cover the pot. Cook, lifting the lid and stirring occasionally, for about 20 minutes, or until the collard greens are fairly tender but not super soft. (Or cook for more or less time! Your call!)
Sprinkle the greens with the vinegar and crisped bacon, stir to combine. Serve hot, spooning up some of the pot likker to serve with the greens.
Notes
Make sure there is no grit in your greens — wash very well in cold water.
Leftover braised mustard greens can be stored in a sealed container in the refrigerator for up to a week. Warm in a pot over low heat, or in the microwave.