In large pot, cook onions in olive oil over medium heat until translucent, about 8 to 10 minutes.
Clean artichokes; hold in lemon water to prevent browning. Trim leaves and stems; quarter and remove fuzz in center; add to onions.
Sauté artichokes and bacon with onions. Season to taste with salt and pepper. Add carrots; cook an additional 2 minutes.
Deglaze pan with wine allowing liquid mixture to reduce by half. Add chicken broth, thyme, bay leaves and pepper. Return to simmer. Cook 10 to 15 minutes or until artichokes are tender. Remove bay leaves and keep warm.
Poach eggs in acidic simmering water (1 teaspoon vinegar per 1 quart water) until whites are set (completely coagulated and firm) and yolks begin to thicken (no longer runny, but not hard). Keep warm.
To serve, portion 2 cups barigoule mixture into shallow bowl; top with poached egg. Garnish with chopped parsley and drizzle with olive oil. Serve immediately.