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Preheat oven to 350 ºF (180 ºC). Gather all the ingredients. Make sure to take the pork out of the refrigerator about 15 minutes before you plan to start cooking. Room temperature meat cook more evenly throughout.
Chop the celery and carrot into small pieces.
Dice the onion. Smash the garlic with the side of the knife.
Dry the pork with paper towel and season all sides with kosher salt and freshly ground black pepper.
Heat a large Dutch oven or cast iron skillet on medium heat. Add 2 Tbsp olive oil and sear the pork on all sides until a crust forms, about 2 minutes per side. Remove the pork from the pan and set it aside.
Lower the heat to medium low, and add a little bit of olive oil if necessary. Sauté the onion and garlic until fragrant and slightly soften.
Then add the celery and carrot.
When the vegetables are well-coated with oil, add 4 Tbsp sake and scrape off the juicy brown bits stuck to the bottom of the pot.
Add 4 Tbsp mirin, 1 tsp brown sugar, and 3 Tbsp soy sauce.
Mix all together and place the pork back in the skillet and spoon some sauce over the pork.
Cover the pork with the oven-safe lid or aluminum foil and roast for 30-40 minutes (30 mins for 1 ½ lb and 40 mins for 2 lb), or until the pork interior temperature reaches about 145 ºF (63 ºC).
Remove the Dutch oven from the oven and transfer the pork to a plate. Cover the pork with foil to keep the moisture and let it rest for about 15 minutes.
Meanwhile heat the Dutch oven on medium low heat. Skim off any foam or scums. Simmer, stirring often, until the sauce has thickened to your preferred thickness. Once the sauce is reduced, the saltiness and flavors will concentrate so adjust how far you want to reduce. Slice the pork against the grain and serve hot with the sauce.