Separate the 3 large eggs into yolks and whites; set the whites aside in a clean bowl for later.
In a large mixing bowl, whisk together 2 cups gluten free all-purpose flour, 1 tablespoon granulated sugar, 1 teaspoon baking soda, 1/2 teaspoon baking powder, 1/2 teaspoon xanthan gum, and 1 teaspoon ground cardamom.
In a separate bowl or measuring cup, combine the egg yolks, the zest of one lemon, and 1 teaspoon vanilla (use the pure vanilla extract, vanilla bean paste, or the scraped seeds of one vanilla pod). Add 1 3/4 cups buttermilk (or the milk + 1 1/2 tablespoons white vinegar mixture left to sit 5–10 minutes) and mix until smooth.
Add 4 tablespoons melted butter (let it cool a few minutes after melting) to the yolk-buttermilk mixture and stir just until combined.
Pour the wet mixture into the dry ingredients and mix gently until the batter is smooth. Small lumps are fine; do not overmix.
Using a clean electric mixer or whisk, beat the reserved egg whites until stiff peaks form.
Gently fold the beaten egg whites into the batter in two additions, using a spatula and folding from the bottom to keep as much air as possible. Stop as soon as the whites are incorporated; some small streaks or lumps are fine.
Preheat your aebleskiver pan over medium-low to medium heat. Add a little butter or oil to each well (butter recommended for flavor) and let it melt and heat through.
Do one test aebleskiver first to confirm the pan temperature. Adjust heat if it browns too quickly (lower) or too slowly (raise slightly).
Fill each well nearly full with batter. Cook until the batter begins to bubble around the edges.
Using a skewer or thin utensil, push against the side of each well and gently turn each aebleskiver 90 degrees so batter flows into the bottom of the well. Wait for bubbling around the edges again, then turn another 90 degrees. Repeat for a third turn, then give a fourth and final turn to form a full sphere. Continue rotating as needed until evenly browned on all sides.
Remove the aebleskiver from the pan and serve immediately while hot.