Preheat oven to 425 degrees. Lightly butter a 13x9x2 baking dish.
In a large skillet heat the olive oil over medium high-heat. Add the onion and season with the thyme and a pinch of salt and pepper. Cook, stirring frequently until golden brown, about 12 minutes. (Turn down heat if browns too fast or burning). Set aside.
Meanwhile, place the potatoes in a saucepan just covered with water. Add a pinch of salt, cover and bring to a boil. Simmer the potatoes until they are al-dente (still slightly firm but cooked 75% of the way through), about 15-20 minutes. Drain the potatoes.
Arrange half of the potatoes on the bottom of the casserole dish. Sprinkle with salt and pepper and parsley. Layer the entire onion mixture on top of the potatoes and then crumble the goat cheese over the onion layer. Top with remaining half of potatoes and spread evenly to cover the cheese. Dot the top of the potatoes with the butter, and pour the milk over the top. Gently press the potatoes down with your hand or a spatula to flatten into the milk and spread evenly. (The milk will not cover the potatoes).
Bake, uncovered, until the milk has mostly evaporated, the side are bubbling, and the edges are starting to turn brown, about 35-40 minutes. Halfway through cooking, use a firm spatula to gently press down the potatoes again into the liquid. Remove from oven and let sit 15 minutes. Serve hot.
Enjoy!
