Preheat oven to 300°F (150°C). Season shank steaks all over with salt and pepper. In a large heavy roasting pan (alternatively, you can use 2 large pots such as Dutch ovens or straight-sided sauté pans, splitting ingredients between them), heat oil over high heat until shimmering. Add steaks, in batches, if necessary, and cook until browned on both sides, about 5 minutes per side. Transfer steaks to a platter

Lower heat to medium-high and add onions, carrots, and garlic and cook, stirring, until softened, 5 to 10 minutes. Add wine, scraping up any browned bits, and bring to a simmer; lower heat to medium and cook until raw alcohol smell has mostly cooked off, about 20 minutes.

Add thyme and bay leaves. Nestle shank steaks in cooking liquid so that they are almost but not completely submerged; pour any accumulated juices from steaks into the roasting pan. Cover with aluminum foil. Transfer to oven and braise until shanks are tender, about 3 1/2 hours, removing foil after 1 1/2 hours.

Discard foil and transfer shanks to a clean platter. Skim rendered fat off surface of braising liquid and discard thyme and bay leaves. Using an immersion blender or blender, blend aromatics and braising liquid to form a smooth sauce. Thin with warm water or stock as needed to create a consistency just thick enough to coat the back of a spoon. Add soy sauce and season with salt and pepper to taste.

Serve shanks with sauce, sprinkling parsley on top. Shanks can be refrigerated in their sauce for up to 4 days. Reheat before serving, and thinning reheated sauce if necessary with water.