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Preheat the oven to 350°F. Grease
a 9-inch bundt or round cake pan. Place the whisk attachment of a stand mixer or the beaters of a hand mixer in the freezer.
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In a food processor, combine the cooked squash, milk, vanilla, and eggs. Process until smooth.
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In a large bowl, whisk together the butter and brown sugar. Add the squash mixture and stir until well combined. In a bowl, combine the flour, baking soda, baking powder, salt, cinnamon, nutmeg, cloves, and ginger. Whisk to combine.
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Fold the dry ingredients into the wet until the batter is mixed thoroughly and without lumps. Pour the batter into the prepared pan. Bake until a wooden skewer inserted into the center comes out clean, 35 to 40 minutes. Let cool in the pan for 10 minutes before inverting onto a wire rack to cool completely.
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Meanwhile, in a small saucepan over medium-high heat, warm the cream with the chai tea bags until very warm but not boiling. When small bubbles form, remove from the heat, cover, and let steep for 8 minutes. Remove the tea bags, squeezing their liquid back into the pot, or strain out the loose tea. Transfer the chai cream to a bowl and chill for 45 minutes.
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With a stand mixer or hand mixer, whisk the sugar and chai cream just until stiff peaks form. Serve with the cake.