In a bowl, combine the cornstarch, broth and water until smooth.
In a large skillet over high heat, brown the white mushrooms in the butter. Add the onion and cook until translucent. Deglaze with the wine and let reduce for 1 minute. Add the broth mixture and morel mushrooms. Bring to a boil, stirring constantly. Simmer for 5 minutes or until the sauce has thickened. Season with pepper.
Using a spoon, gently drop the eggs into a pot of simmering water. Cook for 6 minutes. Rinse under cold running water. Carefully peel the eggs and set aside.
Preheat the oil in a deep fryer to 350°F (180°C). Line a baking sheet with paper towels.
Fry half of the French fries at a time until crisp. Drain on the paper towels and keep warm.
Divide the fries among four bowls and top with the cheese curds, sauce and chives. Place a soft-boiled egg on top of each poutine and carefully cut in half.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.