Preheat the oven to 375°F (190°C). Lightly grease a small to medium baking dish and set aside.

Warm the olive oil in a large skillet over medium heat. Add the onions and shallot, then season with salt, pepper, and sugar.

Cook slowly for about 20–25 minutes, stirring occasionally, until the onions are deeply golden, soft, and sweet.

Stir in the garlic and red pepper flakes, if using, and cook for about 1 minute until fragrant. Remove the skillet from heat.

In a medium bowl, combine the yogurt or sour cream, mayonnaise, grated cheese, and mozzarella. Stir until smooth and evenly mixed.

Fold the warm onion mixture into the creamy cheese base until fully incorporated.

Spoon the mixture into the prepared baking dish and spread it evenly.

Bake uncovered for 22–25 minutes, or until the dip is hot, bubbly, and lightly golden on top.

For extra color, broil briefly at the end if desired.

Let the dip rest for about 5 minutes before serving.