Heat a large skillet over medium heat with the olive oil before adding the diced onions. Sprinkle the Swerve and salt on top of the onions and cover for 5 minutes.
After 5 minutes, stir the onions, cover, and cook another 5 minutes. Repeat until the onions have cooked for 15-20 minutes and begin to turn golden brown. At which point, add the Worcestershire sauce and cook for 2-3 additional minutes.
While the onions cook, mix the Greek yogurt, light mayo, white pepper, garlic powder, and parsley flakes in a large bowl.
Add the cooked onions to the yogurt mixture and stir to fully incorporate. You can serve immediately as a warm dip or refrigerate and serve chilled.