Place butter in a small saucepan over medium heat and let it melt. Stir continuously until it becomes golden brown with small brown specks and a nutty aroma. This step adds deep flavor to the dessert.
Remove the butter from heat and allow it to cool slightly before using it. This prevents the egg from cooking when mixed into the batter. Slightly cooled butter also blends better with the sugar.
In a mixing bowl, combine the brown butter with brown sugar and granulated sugar. Whisk until the mixture becomes smooth and glossy. Add the egg, heavy cream, and vanilla extract, then mix until fully combined.
In another bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon. Mixing these ingredients first ensures they distribute evenly throughout the dough.
Gradually add the dry ingredients into the wet mixture. Stir gently using a spatula until a thick cookie dough forms. Avoid overmixing so the skillet cookie remains soft.
Carefully fold the fresh blueberries into the dough. Stir slowly so the berries stay intact and don’t release too much juice.
Lightly grease a 10-inch cast iron skillet. Transfer the cookie dough into the skillet and spread it evenly so it bakes uniformly.
Drop spoonfuls of blueberry preserves on top of the dough. Use a knife to gently swirl it through the surface for a marbled effect.
Bake the skillet in a preheated oven at 350°F (175°C). Bake until the edges are golden brown while the center remains slightly soft.
Allow the skillet cookie to cool for about 10 minutes. Serve warm with a scoop of vanilla ice cream for the best dessert experience.