Preheat oven to 350°F (175°C). Grease or line an 8×8 or 9×9-inch baking pan.
Mix cake batter: In one bowl, whisk flour, baking soda, baking powder, salt, and pumpkin spice. In another, combine pumpkin puree, sugars, oil, and milk until smooth. Gently fold dry ingredients into wet until just combined.
Make streusel: Toss flour, brown sugar, and pumpkin spice. Cut in cold butter until crumbly.
Assemble: Spread pumpkin batter evenly in the pan, then generously sprinkle with streusel.
Bake 30–35 minutes, or until a toothpick in the center comes out clean. Cool slightly.
Caramel syrup: In a saucepan, melt butter. Stir in buttermilk, sugar, and corn syrup; bring to a boil, then lower heat. Add baking soda, cook 1–2 min until thickened, remove from heat, and stir in vanilla.
Serve: Drizzle syrup over the warm cake, slice, and enjoy!