Preheat the oven to 350 degrees F (175 degrees C). Spray a fluted tube pan (such as Bundt®) with nonstick cooking spray, paying attention to crevices.
Whisk flour, baking soda, cinnamon, nutmeg, pumpkin pie spice, and salt for cake together in a medium bowl.
Beat sugar, oil, and vanilla bean paste together in a separate mixing bowl for 2 minutes. Add eggs, one at a time, beating well after each addition. Alternate adding pumpkin and flour mixture to the sugar mixture. Set cake batter aside.
Combine flour, all of the brown sugar, melted butter, cinnamon, and salt for streusel in a bowl. Sprinkle half of the streusel on the interior of the prepared Bundt® pan, lightly pressing streusel against the sides of the pan. Pour 1/3 of the cake batter into the pan and sprinkle some streusel onto the batter; repeat two more times.
Bake cake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour and 15 minutes.