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Preheat your oven to 350°F (175°C) and grease a 9x13 inch baking dish.
In a large skillet, heat the olive oil over medium heat. Add the sliced onions and sugar, and cook until the onions are caramelized and golden brown, about 15-20 minutes. Stir occasionally to prevent burning.
In a mixing bowl, combine the flour, baking powder, and salt. Add the softened butter and mix until the mixture resembles coarse crumbs.
Gradually add the milk to the flour mixture, stirring until just combined.
Spread half of the batter into the prepared baking dish. Layer the caramelized onions evenly over the batter, then spread the remaining batter on top.
Sprinkle black pepper and fresh thyme leaves over the top, if using.
Bake in the preheated oven for 30-35 minutes, or until the top is golden and a toothpick inserted into the center comes out clean.
Let the cake cool for a few minutes before slicing and serving.
Variations & Tips
For a cheesy twist, sprinkle some shredded cheddar or Swiss cheese over the onions before adding the top layer of batter. You can also add some cooked bacon or ham for extra flavor. If you're a fan of herbs, try adding rosemary or sage instead of thyme. For a gluten-free version, use a gluten-free flour blend in place of the all-purpose flour