Heat a large Dutch oven or other large pot over medium-high heat. Fry the bacon until it’s starting to brown, about 5 minutes.
Reduce the heat to medium; add the onion. Cook stirring regularly, until the onion softens, about 7-10 minutes. Add the garlic and cook until fragrant, about 45-60 seconds.
Add the tomatoes with their juices, broth, and red pepper. Bring to a boil, then reduce the heat to maintain a simmer. Cook, stirring occasionally, for 20 minutes.
Return the liquid to a boil. Add the chopped collard greens in batches, waiting until they wilt to add the next batch. Stir in the vinegar, brown sugar, and salt to taste.
Cook, stirring occasionally, until the greens are just tender, about 15-20 minutes. Taste and season with additional red pepper flakes, brown sugar, or salt, if desired.
