Arrange a rack in the upper third the oven and preheat to 425 degrees F.
Cut the beet into 1/4-inch thick slices. Using a jack-o'-lantern cookie cutter, cut the beet slices into jack-o'-lanterns and set aside.
Place the salmon on a foil lined baking sheet, lightly brush with oil, and season generously with salt and pepper. Roast the salmon until just cooked through, about 15 minutes.
Meanwhile, combine the vinegar, water, lemon juice, and brown sugar in a saucepan. Bring to a boil and cook, stirring occasionally, until thickened and reduced to glaze.
Carefully transfer the salmon to a serving platter and arrange some of the beet jack-o'-lanterns in a row down the center of the fillet. Spoon the glaze over the top. Serve hot or at room temperature.