Preheat oven to 400 degrees F (200 C).
Remove tough ends of Brussels sprouts and halve them. Try to keep them evenly sized; quarter very large ones if necessary.
Place Brussels sprouts onto a baking tray. Add vegetable oil, salt, and pepper. Toss to mix well. Bake on the middle rack of oven for 15 minutes. Toss again and flip to bake the other side, 10 to 15 minutes, until crispy and cooked through.
While baking Brussels sprouts, prep and cook the sauce. Heat olive oil in a small saucepan over medium heat. Add garlic and shallot. Stir and cook until the herbs start to sizzle. Add dried plums and stir a few times. Turn to medium low heat. Add curry powder. Cook until the ingredients are evenly coated with curry, 1 minute. Add balsamic vinegar, soy sauce, and sugar. Continue cooking until bringing to a boil. Let cook for another minute or two, until the sauce thickens.
Right before serving, place the Brussels sprouts in a bowl and add the plum sauce. Gently toss a few times and serve immediately as an appetizer or side dish.