Trim the base of the romaine hearts, then cut them lengthwise in half. You will have two large wedges.
Cut the beets in half lengthwise, then angle your knife to slice the halves into ¼-thick wedges.
Arrange the romaine hearts on a platter. Carefully scatter the roasted beets over the center of the wedges, followed by the pistachios and the basil leaves. Right before you’re ready to serve, drizzle the vinaigrette over the top. Season with salt and pepper and serve family-style.