Preheat the oven to 350°F (175°C) and prepare an 8x8-inch square baking vessel with parchment lining or non-stick spray.
Formulate the streusel topping by integrating 0.25 cup flour, 0.25 cup coconut sugar, rolled oats, and 1.5 teaspoons cinnamon with solid-state coconut oil until a heterogeneous crumb texture is achieved.
In a primary mixing vessel, emulsify the unsweetened applesauce, plain Greek yogurt, 1 cup coconut sugar, eggs, and vanilla extract until the mixture is homogenous and devoid of yogurt lumps.
Incorporate 1.5 cups whole wheat pastry flour, baking powder, baking soda, salt, 2 teaspoons cinnamon, and nutmeg into the wet phase using a folding technique to prevent gluten over-development.
Transfer approximately 50 percent of the batter into the prepared baking vessel, spreading it into a uniform layer with a spatula.
Distribute 50 percent of the prepared streusel mixture evenly across the batter surface to create a central cinnamon layer.
Layer the remaining batter carefully over the streusel, followed by a final top coating of the remaining streusel mixture.
Execute thermal processing in the oven for 30 to 35 minutes until a mechanical probe inserted into the center emerges clean.
Allow the cake to rest for 15 minutes to reach thermal equilibrium before portioning into nine equal square units.