Add the pumpkin puree and whisk until incorporated.
Pre-heat the oven to 350ºF. Open the condensed milk can and pour the milk in an oven proof pan and cover with foil. Place this pan in a larger pan, and fill the larger pan with water to form a water bath. Bake for about 3 hours. Baking time will vary depending on how much condensed milk you are baking at a time. As you bake, stir every 45 minutes or so, making sure the water from the bottom pan isn’t evaporating. If it evaporates, replace with more water so the dulce de leche doesn’t scorch on the sides of the pan. Remove from the oven when the dulce de leche is thick, the color is a deep caramel shade. The dulce de leche will get even thicker as it cools down once you let it rest in the fridge for a few hours before using it.
If the dulce de leche is too lumpy, I recommend letting it come to room temperature after baking it, and then placing it in a food processor or blender, and processing it until it becomes smooth, otherwise the frosting will turn out lumpy.
Dulce de Leche: You can find more ways of making Dulce de Leche here. Or you can use store-bought. You will need about 1 1/3 cups of dulce de leche for the whole recipe.
Pumpkin Puree: Make sure to use pumpkin puree, not pumpkin filling. Pumpkin puree is made of 100% pumpkin.
Russian Buttercream: If the buttercream is too runny and soupy and not coming together, place the bowl in the fridge for 5 to 10 minutes and then try whipping it again. It could be due to the butter being too warm, which is why it's important to take the temperature of the butter before starting.
Recipe Time: The time accounted above is considering the dulce de leche is already made. You should make the dulce de leche a day before starting this recipe, if going the homemade route.