Preheat the oven to 350°F (175°C). Grease a 9x9-inch baking dish or springform pan with butter or nonstick spray, or line it with parchment paper for easy removal. Set aside.

Prepare the crumble topping: In the bowl of a stand mixer fitted with the paddle attachment, combine the softened butter and brown sugar on medium speed for about 2–3 minutes, until smooth, creamy, and well blended. Add the cinnamon and gluten-free flour, then mix on low to medium-low speed just until the mixture comes together and forms large, crumbly clumps. Avoid overmixing—you want some texture. Scrape down the sides of the bowl as needed, then set the crumble aside while you make the cake batter.

Make the pumpkin cake batter: In a large mixing bowl, whisk together the cane sugar and melted butter until fully combined and slightly glossy. Add in the eggs, pumpkin puree, sour cream, apple cider vinegar, and vanilla extract. Whisk until smooth and creamy.

Combine the dry ingredients: In a separate medium bowl, whisk together the gluten-free flour, baking powder, baking soda, cinnamon, ginger, nutmeg, cloves, and salt until evenly distributed.

Mix wet and dry ingredients: Gradually add the dry mixture to the wet ingredients, folding gently with a rubber spatula or wooden spoon until no dry streaks remain. Be careful not to overmix—this keeps the cake soft and tender.

Assemble the cake: Pour the batter evenly into the prepared 9x9-inch baking dish. Use a spatula to smooth the top. Evenly sprinkle the crumble topping over the batter, breaking up any large chunks as desired.

Bake: Place the cake in the preheated oven and bake for 45–50 minutes, or until a toothpick inserted in the center comes out mostly clean with a few moist crumbs (not wet batter).

In a medium bowl, use a handheld mixer or whisk to beat the softened cream cheese until smooth and creamy.

Add the powdered sugar and mix on low speed until combined, then increase to medium-high and beat until fluffy.

Mix in the vanilla extract and 1 tablespoon of milk. If the glaze is too thick, add more milk 1 teaspoon at a time until it reaches a smooth, pourable consistency.

Allow the cake to cool in the pan for at least 20–30 minutes. Drizzle the glaze over the top using a spoon or piping bag. Let it set for 5–10 minutes before slicing. This helps the crumb set and makes cutting easier. Serve warm or at room temperature with a cup of coffee or tea.