Preheat the oven to 350°F (175°C) and line a 9x13-inch baking pan with parchment paper.
In a small bowl, stir together ¾ cup (120ml) milk and 1 Tbsp apple cider vinegar, then set aside for 10 minutes to curdle.
In a medium bowl, whisk 2¼ cups (300g) gluten-free 1:1 flour, ¼ cup (30g) cornstarch, 2 tsp baking powder, ½ tsp baking soda, ½ tsp salt, 1½ tsp cinnamon, 1 Tbsp pumpkin pie spice, and ½ tsp nutmeg.
In a large mixing bowl, beat ½ cup (110g) unsalted butter, ⅓ cup (75g) vegetable oil, and 1¾ cups (350g) sugar until pale and fluffy, about 2–3 minutes.
Add 4 large eggs, one at a time, mixing well after each, then beat in 1 Tbsp vanilla extract.
Mix in 1 can (15 oz / 425g) pumpkin purée until smooth.
Add half the dry ingredients, mix gently, then stir in the milk mixture. Add the remaining dry ingredients and mix just until combined — don’t overmix.
Spread the batter into the prepared pan and bake for 35–40 minutes, or until a toothpick in the center comes out clean.
Cool in the pan for about 10 minutes.
2
Churro Topping
While the cake is still warm, brush the top with ¼ cup (55g) melted butter.
In a small bowl, combine ½ cup (100g) sugar with 1 Tbsp cinnamon and sprinkle evenly over the cake.
3
Brown Butter Icing
In a small saucepan, melt ½ cup (110g) unsalted butter over medium heat and cook until golden brown and nutty.
Let it cool for 5 minutes, then whisk in 2 cups (240g) powdered sugar, 2–3 Tbsp milk, 1 tsp vanilla extract, and a pinch of salt until smooth.
If needed, add a little more milk to thin it out.
Drizzle the icing over the cooled cake.
4
Vanilla Bean Buttercream (Optional)
Beat ½ cup (113g) softened unsalted butter until creamy, about 2–3 minutes.
Slowly mix in 3 cups (330g) powdered sugar, then add ½ Tbsp vanilla bean paste and 2 Tbsp milk.
Whip on medium-high speed for 5–7 minutes until light and fluffy.