Thoroughly grease a 6-cup Bundt pan and set aside.
To make vegan eggs, combine 4 tablespoons of egg replacer with 1 cup of water. Mix well and let sit for one minute to thicken. Then beat together the vegan egg mix, pumpkin purée, oil, sugars, and vanilla extract in a large mixing bowl until well blended.
Stir in the flour, baking soda, baking powder, salt, and spices into the wet ingredients, folding gently to combine. Set aside.
Make the Filling
Whisk together the brown sugar, cinnamon, and espresso powder in a small mixing bowl. Set aside.
Assemble the Cake
Spoon one-third of the cake batter into the bottom of the prepared pan. Sprinkle half the filling on top. Spoon another third of the batter into the pan and sprinkle with the remaining filling. Spread the remaining batter on top, smoothing it with a spatula.
Bake the cake for about 60 minutes, or until a toothpick inserted in the centre comes out clean. Then, remove the cake from the oven and cool in the pan for 15 to 20 minutes before turning it out onto a rack to cool completely.
Serve as is or with confectioners' sugar. Store any leftovers in an airtight container at room temperature for several days.
Notes
The pictured cake was made in a 6-cup Bundt pan; however, a 10-cup Bundt pan would suit.