Preheat the oven to 400˚F. Butter a 9-inch shallow pie plate or skillet and set aside.
Trim the tops and bottoms of the potatoes and discard. Slice the potatoes into rounds about ½-inch in width. Heat two tablespoons of the olive oil in a large skillet over medium heat. Add the potato rounds in an even layer, along with ¼ cup water, and season generously with salt. Cook for 10 minutes, without disturbing, then flip. Add another ¼ cup water, and cook for an additional 10 minutes, or until the potatoes are fork tender, but not falling apart. Transfer the potatoes to a paper-towel lined plate and set aside.
Add the remaining tablespoon of olive oil to the same skillet and return to medium heat. Sauté the onion, garlic and thyme until softened, but not browned, about 6 – 8 minutes. Add the balsamic vinegar and sauté for another minute. Transfer the onion mixture to a bowl and set aside.
Arrange the cooked potato rounds in an even layer in the prepared pie plate and scatter the cubes of butter over the top. Top with an even layer of the onion mixture and sprinkle with the cheese. Top with the sheet of puff pastry and tuck the edges into the sides of the tin. (If you find the pastry is too small to fully cover the cheese, you can gently roll it out on a lightly dusted work surface).
Transfer the tart to the preheated oven and bake for 25-30 minutes, or until the pastry is cooked through and golden brown. If you find the pastry is getting too browned before it has finished cooking, you can cover the tart loosely with aluminum foil.
Remove the tart from the oven and allow to rest for 5 – 10 minutes. To serve, place a serving plate on top of the puff pastry and carefully invert the tart out of the pie plate. Garnish with a handful of watercress or arugula leaves and a drizzle of balsamic glaze.