Upside Down Cookie Tart

Name: Upside Down Cookie Tart
Yield: 0
Cuisine: american
Ingredients: 1 3/4 cups plus heavy cream 1/2 cup, divided; 2 tablespoons sugar; 1 teaspoon vanilla extract; 9 ounces milk cookies; Milk, as needed; 7 ounces dulce de leche; 5 ounces dark chocolate; 1/2 cup heavy cream; 1/2 cup dark chocolate shavings