Preheat the oven to 300 degrees F.
Dry short ribs with a paper towel to remove as much moisture as possible. Season them with salt and pepper.
Heat oil in a large Dutch oven over medium-high heat until shimmering. Working in batches so all the short ribs fit in a single (not too crowded layer), sear on all sides, about 4-8 minutes per side, until a nice brown crust has formed.
Transfer browned short ribs to a platter and repeat with remaining short rib until all done.
You’ll have some good browned bits left behind in your Dutch oven (we want ‘em!). Reduce heat to medium and add garlic, cut side down, and cook, undisturbed, 2-3 minutes, until golden brown. Add onion, celery and carrots; season with salt and pepper. Toss to coat veggies with the oil left behind from the short tibs and cook, stirring occasionally, until softened and just beginning to brown, about 6-10minutes. Add tomato paste, stir to coat and prevent any scorching; cook until tomato paste has started to caramelize at the edges, about 2-3 minutes.
Add dry red wine and port, scraping up any browned bits from the bottom and sides of pot. Let simmer for 3-5 minutes.
Add stock, return short ribs to pot along with any accumulated juices, meat side down, nestling them so that they’re submerged in the braising liquid. Add thyme and bay leaves, bring to a simmer, cover, and transfer to oven.
Cook, undisturbed, until short ribs are meltingly fall of the bone tender, 2 ½ -3 ½ hours (exact timing will depend on how thick you’re short ribs are).
Using tongs, carefully remove short ribs from pot and transfer to a plate.
Stain braising liquid through a strainer set on over a large, heatproof bowl, (the vegies have turned mushy and we’ve used all their flavor), extracting as much braising liquid as possible.
Return braising liquid back to Dutch oven (may want to wipe it clean – personal preference), add brown sugar and fish sauce and bring to a gentle simmer.
Simmer until braising liquid is thick enough to coat the back of a spoon, about 40 minutes.
Season sauce with salt and pepper to taste. Return short ribs to Dutch oven, spooning the sauce all over and around them to glaze and rewarm.
Top with fresh herbs such as parsley and chives (optional) and serve.