Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan with 1 teaspoon butter.
Mix pumpkin puree, eggs, water, 1 tablespoon vanilla extract, and pumpkin pie spice together in a large bowl. Stir in yellow cake mix and baking soda until just combined. Pour batter into the prepared baking pan.
Mix 1/2 cup brown sugar, flour, and melted butter in a small bowl until crumbly; sprinkle over the batter with your fingers.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 25 to 30 minutes.
Combine 1/2 cup brown sugar, heavy cream, white sugar, and 1 teaspoon vanilla extract in a saucepan; bring to a simmer over medium heat. Remove from heat and stir until brown sugar and white sugar are dissolved and glaze is smooth.
Poke holes all over the top of the cake with a toothpick. Pour glaze evenly over cake.