Using a food processor, pulse together the flour, sugar and salt until combined. Add butter and pulse until mixture becomes coarse meal, about 15 pulses. In a small bowl, combine egg yolk and water. Add the egg mixture to food processor and pulse until it starts to clump together. DO NOT pulse until ball is formed. It should be crumbly with large clumps of dough.
Turn dough only a lightly floured surface and form into a ball. Flatten slightly to form a disk. Wrap in plastic wrap and put in fridge for at least 1 hour or up to 3 days.
On a lightly floured surface, roll the dough into a circle slightly larger in diameter than the 9 inch tart shell. Press dough into the tart shell, trimming the edges with a sharp knife. Cover with plastic wrap and place in fridge for at least 30 minutes or until firm.
While the crust is chilling, preheat oven to 350°F and place baking sheet in the oven. Crunch up some parchment paper and line pie crust with it. Fill with pie weights, dried beans or rice, making sure they are evenly distributed.
Place tart on preheated baking sheet and bake until the edges of the crust are beginning to brown, about 20 minutes. Remove the tart from the oven and take out the parchment paper with the weights. Poke holes around the bottom of the crust with a fork and place back in the oven, baking for another 10 minutes, or until the bottom is golden brown.
While the tart crust is baking, make the caramelized onions. Heat large skillet over medium heat and add the butter. Once melted, add the sliced onions and salt. Cook and stir every 5 to 10 minutes until the onions are soft and deeply browned. It should take about 20 minutes total. Add garlic in the last 2 minutes. Add 2 tablespoon water to deglaze the pan. Set aside.
Now make the filling. Put the goat cheese in a food processor and pulse until it becomes crumbly. Add the cream, eggs, thyme and salt then blend until smooth and well combined.
Scatter the caramelized onions over the bottom of the tart shell. Pour the goat cheese mixture over the onions to fill the tart shell (if the shell has shrunk, you may have extra filling). Bake for 30 to 40 minutes, until the tart is set when gently shaken and the top is golden brown. Let cool for 10 minutes before serving warm or at room temperature.