Prepare a pastry crust, gluten-free and vegan if preferred, and keep chilled until ready to assemble. See here for a gluten-free pastry recipe!
Preheat oven to 425 degrees F. Wrap beets in foil and place in oven. Roast for about 30 minutes, or until you can easily pierce the beets with a knife. Let cool and remove the skin. Cut the beets into 1-inch cubes. Set aside.
Lower heat of oven to 350 degrees F.
In a large skillet, heat the brown sugar. As it starts to melt, add the butter or butter substitute, continuously stirring. Add the beets and sliced red onion, keeping the pan over medium-high heat for 10-12 minutes. They should start to caramelize. Add the balsamic vinegar and continue heating for a few more minutes until you get a thick sauce.
Lightly grease a cake pan with butter or butter substitute. Place the beets and onions at the bottom of the pan. This will end up being the top of the tarte, so feel free to create a design here. Add the sauce from the skillet over the roots. Roll out the cold pastry dough and lay it over the pan. Tuck in the edges. Using a knife, slice small ½ - 1-inch marks in the dough. Bake the tarte in the oven for 25-30 minutes. Let cool for at least 10 minutes and then carefully invert onto a serving plate. Top with black pepper, lemon zest, and fresh parsley. If not vegan, serve with a sprinkle of fresh chèvre