For the strawberries: Toss together the strawberries, granulated sugar and vinegar in a small bowl. Allow the mixture to stand for 15 minutes. Strain before using.
For the omelet: Whisk together the eggs, granulated sugar, cream and salt until smooth in a medium bowl. Stir in the mint. Heat the butter and oil over medium-high heat in a 10-inch nonstick skillet. Add the egg mixture and cook until almost set, about 4 minutes. Spoon the strawberry mixture down the center of the omelet. Fold the edges of the omelet over the strawberries. Cook until the egg mixture has set, 3 to 4 minutes.
For the whipped cream: Beat the cream, powdered sugar and vanilla in a large mixing bowl until the cream holds stiff peaks.
Cut the omelet into slices and serve with whipped cream.