Heat the butter or olive oil in a large skillet over medium heat.
Add the sliced onions to the skillet, add salt and cook them slowly, stirring occasionally, until they become caramelized and golden brown. This process can take around 30-40 minutes.
Remove the caramelized onions from the heat and let them cool.
In a mixing bowl, combine the Greek yogurt, mayo, softened cream cheese, Worcestershire sauce (or gluten-free soy sauce), garlic powder, salt, and pepper. Mix well until smooth.
Reserve one tablespoon of the caramelized onions, add the rest to the yogurt and cream cheese mixture. Stir until the onions are evenly distributed throughout the dip.
Taste and adjust the seasonings if needed.
Transfer the dip to a serving bowl and refrigerate for at least 1 hour to allow the flavors to meld together.
Serve the keto caramelized onion dip with your favorite low-carb chips, vegetable sticks, or keto-friendly crackers.