Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking pan.

In a medium bowl, whisk together the flour, baking powder, baking soda, ground cinnamon, nutmeg, and salt.

In a large bowl, cream together the granulated sugar and softened butter until light and fluffy.

Add the eggs, pumpkin puree, and vanilla extract to the butter mixture, mixing until well combined.

Gradually add the dry ingredients to the wet ingredients, alternating with the buttermilk. Mix until just combined.

In a separate bowl, prepare the streusel topping by combining the brown sugar, rolled oats, ground cinnamon, and melted butter. Mix until crumbly.

Pour half of the coffee cake batter into the prepared baking pan and spread evenly.

Sprinkle half of the streusel topping over the batter.

Pour the remaining batter over the streusel layer and spread evenly.

Top with the remaining streusel mixture.

Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.

Allow to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.