01 - Preheat oven to 375°F. Roll out pastry to line a 9-inch tart tin. Press pastry gently into the tin, trim excess, and prick base with a fork. Chill in refrigerator for 10 minutes.
02 - Line pastry shell with parchment paper and fill with baking beans. Bake for 15 minutes, then remove beans and parchment. Continue baking for 5 minutes until pastry is lightly golden. Set aside to cool.
03 - Heat olive oil and butter in a large skillet over medium-low heat. Add sliced onions, sugar, salt, and pepper. Cook while stirring frequently for 20 to 25 minutes until onions are soft and golden. Stir in thyme leaves and cook for an additional 2 minutes. Remove from heat and let cool slightly.
04 - Whisk together eggs, double cream, whole milk, ground nutmeg, salt, and pepper in a mixing bowl until combined.
05 - Evenly spread caramelized onions over the blind-baked pastry base. Distribute crumbled goat cheese on top. Pour the egg and cream mixture over the filling evenly.
06 - Bake in preheated oven for 25 to 30 minutes or until filling is set and golden on top. Allow to cool for 10 minutes before slicing.
07 - Optional: Garnish with extra thyme sprigs and fresh arugula. Serve warm or at room temperature.