Step 1Put the beets in a medium saucepan and add enough cold water to cover by 2 inches. Generously salt the water. Bring to a boil over high heat, then reduce the heat to maintain a steady simmer. Simmer until a paring knife pierces a beet easily, about 25 minutes. Drain well.
Step 2When the beets are cool enough to handle, peel them, then cut into ½-inch wedges. Stir the vinegar and sliced shallot in a medium bowl and add the beets. Fold until evenly coated, then cover and marinate for a few hours at room temperature or refrigerate for up to 2 days.
Step 3Cut the thick chard stems apart from the leaves, then slice into 1-inch pieces. Grab the stack of leaves and tear them in half crosswise.
Step 4Put the fennel seeds, cinnamon stick, and star anise in a tea strainer or wrap in cheesecloth and tie shut.
Step 5Heat the oil in a wok or saucepot over high heat. When it’s so hot it shimmers, add the diced shallot and cook, stirring, until the sizzling edges brown, about 30 seconds. Add the chard stems and leaves and turn with chopsticks or tongs until wilted, 1 to 2 minutes. Add the soy sauce, rice wine, and ¾ cup water. Stir to mix well, then sprinkle with sugar and stir again. When the liquid comes to a boil, nestle the bundled spices in.
Step 6Reduce the heat to low to maintain a gentle simmer and cover. Simmer until the stems and leaves are very tender, about 20 minutes.
Step 7Remove the tea strainer and discard the spices. Transfer the vegetables to a serving dish with a slotted spoon. If there’s a lot of liquid left in the wok, raise the heat and boil the liquid until it’s reduced to ¼ cup. Drizzle all over the vegetables. Serve hot, warm, or at room temperature.