Preheat the oven to 350°F.
Mix the Just Egg and applesauce together in a measuring cup before adding to the mixing bowl later.
Add the butter and sugar into a mixing bowl or the bowl of a stand mixer. Beat together for 3 minutes or until light and well combined.
Next add in the Just Egg and applesauce mixture about a half or third at a time. Allow to fully incorporate until smooth before adding each additional portion. If the ingredients aren't all at room temperature, the mixture will split and be chunky at this step.
Alternate adding the orange juice and flour a third at a time. I just estimate. Basically don't add all of each all at once. Add a bit of the orange juice and allow to fully incorporate. Then add in some of the flour. Continue alternating until everything is smooth and combined. Don't forget to scrape the sides and bottom of the bowl and mix for another two minutes to make sure everything gets mixed in properly.
Pour the cake batter into the prepared cake pan.
Place the pan on the middle rack of the oven and bake for 32-35 minutes. The top should be golden and the edges will be brown and pulled away from the edge of the pan.
Flip the cake over and onto a plate.