Heat a large dutch oven over medium high. Add butter and heat until it foams and subsides (or heat other fat until shimmering). Add the onion to the fat and sauté, stirring occasionally, until translucent, 5-7 minutes.
Add the garlic and sauté, stirring continuously, until fragrant, about 1 minute.
Deglaze the pot with the red wine and cook until the wine stops bubbling.
Add the pulled pork, carrots, diced tomatoes, balsamic vinegar, rosemary, thyme, bay leaf, salt and pepper to the dutch oven and give everything a good stir.
Reduce heat to medium low, then cover and simmer, stirring occasionally, until the sauce is a deep red, 20-25 minutes.
Fish out the bay leaf and thyme and rosemary stems. Taste for seasoning and add additional salt and pepper if needed.
Ladle over cooked pasta, polenta, spaghetti squash, or zucchini noodles.