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Add water to a medium-sized saucepan and set on a burner on the stove over medium heat.
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When the water starts simmering, place a large glass bowl on top of the saucepan and add the cocoa powder, butter, and sugar to the bowl. Allow the butter to melt and combine with cocoa powder and sugar. It may take around 10 minutes for the butter to melt and combine with the ingredients.
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Remove the bowl from the saucepan and place the bowl onto a towel on your countertop. Whisk in the hot water until combined. Allow the mixture to cool for about 10 minutes before adding the eggs.
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After the mixture has cooled, whisk in 1 egg at a time until combined. Then add in the vanilla extract and whisk to combine.
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Next, whisk in the baking soda and sea salt. Lastly, slowly whisk in the gluten-free flour. Whisk just until the batter is combined.
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Pour and spread the brownie batter into the prepared baking pan. Spoon the sweet potato mixture in several mounds on top of the brownie batter. Use a thin butter knife to gently swirl the sweet potato mixture into the brownie batter.
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Tap the pan against the countertop a few times to remove any air bubbles trapped in the batter.
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Bake for 35 minutes or until the center is set. Remove the pan from the oven and cool on a baking rack.
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Let the brownies cool completely before cutting and serving.