Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan with 1 teaspoon butter.

Combine pumpkin puree, eggs, water, 1 tablespoon vanilla extract, and pumpkin pie spice in a large bowl. Stir in cake mix and baking soda until just combined. Pour batter into the prepared baking pan.

Combine 1/2 cup brown sugar, flour, and 1/4 cup melted butter in a small bowl until crumbly; sprinkle over batter with your fingers.

Bake in the preheated oven until a toothpick inserted into 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; stir until sugars are dissolved and glaze is smooth.

Poke holes all over top of cake with a toothpick. Pour glaze evenly over cake.