To make the cream cheese filling, beat the cream cheese, and sour cream in a mixing bowl with a hand mixer until smooth and fluffy. Add vanilla extract, confectioners sugar, and cinnamon and mix together until combined.
In a small bowl combine brown sugar and cinnamon. Add melted butter to a 9 x 13 baking dish, coating the bottom. Add half the cinnamon sugar mixture evenly on top of the melted butter.
Cut the brioche slices in half. Spread a generous amount of the cream cheese mixture between two halves, creating 10 half sandwiches.
Combine the Just Egg and nondairy milk in another bowl or dish where you can dip the brioche sandwich halves. Dip the brioche sandwiches in this mixture and allow to soak for about 30 seconds. Then place crust sides up in the baking dish. Pour any remaining Just Egg mixture evenly on top of the bread and sprinkle the remaining cinnamon sugar mixture evenly on top. Refrigerate for 30 minutes before baking.
When ready to bake preheat the oven to 375°F. To make the cinnamon crunch topping, melt the butter in a bowl in the microwave and then combing with brown sugar, cinnamon and flour until you have a smooth paste. Dollop all over the top of the bread slices.
Cover the entire dish with foil and bake for 25 minutes, uncover and bake another 25 minutes. Serve with dollops of vegan yogurt or whipped cream, a drizzle of maple syrup and another sprinkle of cinnamon.