Season the pork shoulder cubes with salt and pepper. Heat the vegetable oil in a large skillet over medium-high heat and brown the pork in batches until golden on all sides.
Transfer the browned pork to the slow cooker. Add the chopped onion, minced garlic, grated ginger, and daikon pieces.
Pour the chicken broth over the ingredients in the slow cooker. Stir gently to combine.
Cover and cook on low for 7 to 8 hours until the pork is very tender.
In the last 15 minutes of cooking, ladle about 1 cup of the hot broth into a small bowl and whisk in the miso paste until smooth. Stir the mixture back into the stew.
Taste and adjust seasoning with salt if needed. Serve the stew hot, topped with the sliced scallions.