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Whisk together the flours, sugar, baking powder, salt, cardamom and ground vanilla beans (if using vanilla extract, add with liquids) in a medium-large bowl. Set aside.
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In a small bowl, whisk together the eggs, half and half, sour cream and oil.
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Fold the liquids into the dry ingredients. When they are mostly but not completely combined, add the melted ghee and fold everything together until it is completely blended--some lumps are ok though, do not over-mix.
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Cook the pancakes one at a time on a hot griddle with a tiny (about half teaspoon) bit of melted ghee brushed over the griddle (or nonstick pan). When the edges of dried out and the center has bubbled a bit, flip the pancake and brown the other side (it often takes me a pancake or two to discover the perfect temperature to be cooking them at).
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Serve hot with salted butter and maple syrup.