Preheat the oven to 375 degrees F (190 degrees C). Grease a 9x13-inch cake pan.

Beat butter and brown sugar together with an electric mixer until creamy. Beat in eggs one at a time. Add pumpkin butter and vanilla extract.

Mix flour, baking soda, baking powder, cinnamon, nutmeg, ginger, and salt in a bowl. Stir into the butter mixture.

Spread cake batter in the prepared cake pan. Mix brown sugar, butter, pumpkin butter, and cinnamon together to make topping. Spread topping over the cake batter.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 20 to 25 minutes.