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Place the butter in a medium saucepot over medium-low heat. The butter will melt, and then start to bubble and splatter. Swirl the pan from time to time to stir the butter. Once the bubbling and splatter slows down, you’ll notice the butter start to brown and take on a nutty aroma. Let it go just a little longer to deepen in color and flavor. Keep a very close eye on it, as you don’t want it to burn! If you aren’t sure if it’s brown enough, take a spoonful of the butter and transfer it to a bowl - you’ll be able to see the color better. If it’s a deep brown and smells nutty (not burnt!) then you’re good to go. If it’s still pale, let it brown a little longer. Pour the butter into a bowl and set it aside to cool.
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In a medium bowl combine the flour, cream of tartar, baking soda, salt, and spices. Stir the mixture to evenly distribute the ingredients. Set aside.
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In a large bowl, whisk together the brown sugar, granulated sugar, egg, pumpkin puree, and vanilla extract. Stir in the cooled brown butter.
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Using a spatula, gently mix in the dry ingredients to the wet ingredients. Stir until just combined – the dough will be slightly thick and sticky, but still soft.
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Divide the dough into 2 pieces and place each one a piece of plastic wrap. Form the dough into a log and wrap it up. Refrigerate for 2 hours. The dough will seem very soft, but it will firm up in the refrigerator.
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Preheat oven to 350º.
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Line 2 baking sheets with a silpat or parchment paper.
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Combine the granulated sugar and cinnamon in a small bowl or plate.
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Remove one log of dough from the refrigerator and slice it into ½-inch thick slices. You should get around 14 slices per log – don’t worry about being too precise here!
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Toss the slices in the sugar/cinnamon mixture to coat and place them on your baking sheets – leaving ¾ - 1-inch between each.
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Bake the cookies for 10-12 minutes, or until they are crackled and set. Let them rest on the baking sheet for 2 minutes before transferring them to a cookie rack to cool completely. Drizzle the cooled cookies with the homemade caramel.
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The cookies will keep in an airtight container for up to 1 week.