01 - Preheat the oven to 375°F. Roll out pastry to fit a 9-inch tart tin, press into tin, trim edges, and prick base with a fork. Refrigerate for 10 minutes.
02 - Line the pastry with parchment paper and fill with baking beans. Bake for 15 minutes, remove beans and parchment, then bake for an additional 5 minutes until golden. Set aside.
03 - Heat olive oil and butter in a large skillet over medium-low heat. Add onions, sugar, salt, and pepper, stirring frequently for 20 to 25 minutes until onions are soft and golden. Stir in thyme and cook for 2 more minutes. Remove from heat and let cool slightly.
04 - In a mixing bowl, whisk together eggs, heavy cream, milk, ground nutmeg, salt, and pepper until fully combined.
05 - Evenly spread the caramelized onions over the baked tart base, scatter crumbled goat cheese on top, then pour the egg mixture evenly over the filling.
06 - Bake in preheated oven for 25 to 30 minutes until the filling is set and lightly golden. Allow to cool for 10 minutes before slicing.
07 - Decorate with additional thyme sprigs and fresh arugula if desired. Serve warm or at room temperature.