About 30 minutes – 1 hour before you’d like to begin cooking, pull the beef short ribs from the refrigerator and allow them to come up to room temperature. Just before cooking, use a paper towel to pat the ribs as dry as possible. Season liberally with kosher salt and ground black pepper; a good rule of thumb is 1 teaspoon kosher salt per pound of short ribs.
Add the vegetable oil to a large, heavy-bottomed pot with a tight fitting lid over medium-high heat (I use a 5-qt Dutch oven). Once the oil is hot and shimmering, carefully add in the seasoned short ribs – work in batches, if necessary, to avoid overcrowding the pot. Cook for 3-4 minutes per side, until browned well. Transfer the browned short ribs to a plate and set aside. Repeat with any remaining short ribs as needed. Once all of the short ribs are browned, carefully drain off the drippings from the pot and discard or reserve for later use.
Nestle the browned short ribs in the Dutch oven, topping with the sliced ginger, garlic, and green onions. Prepare the braising liquid by by whisking together the dark brown sugar, shoyu, beef broth, and dry sherry until the sugar is dissolved. Pour over the short ribs. Return the pot to medium-high heat. Once boiling, reduce heat to maintain a gentle simmer. Cover the pot and braise for 3 – 3 ½ hours, until the short ribs are fall off the bone tender. (See Recipe Notes for alternate cooking methods.)
If needed, wipe out the inside of the Dutch oven, then return to the stove over medium-high heat. Pour the strained soy braising liquid into the Dutch oven. While whisking constantly, slowly pour in the prepared cornstarch slurry. Continue whisking until the sauce is thickened and glossy. Once the sauce comes to a boil, reduce to low heat and return the cooked short ribs to the Dutch oven. Allow everything to simmer together for 2-3 minutes, just until warmed through.