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Special equipment: 10-inch round cake pan
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Preheat the oven to 375 degrees F. Grease the sides and bottom of a 10-inch round cake pan with butter.
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For the filling: In a bowl, add the brown sugar, pecans, diced apple, lemon zest, cinnamon, nutmeg, cardamom and a pinch of salt.
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Stir until combined.
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In a small pot, melt the 2 tablespoons butter with a pinch of salt.
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Lightly dust a clean work surface with flour.
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Flatten the puff pastry and roll with a rolling pin to even out and seal the perforations, if any.
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Brush the butter all over the puff pastry, leaving a 1-inch border at one of the shorter ends.
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Sprinkle the apple-cinnamon mixture evenly over the pastry sheet, being careful to leave that 1-inch border.
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Starting from the end furthest from the edge without any filling, begin to tightly roll the pastry.
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Tuck and press as you go, keeping the log as even as possible.
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When the edge is reached, roll the pastry onto itself and press firmly, even pinching, to seal.
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Using a serrated knife, trim the edges and gently cut 6 equal slices from each log.
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Repeat with the second puff pastry sheet to make 12 pieces total.
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Place the slices spiral side up in the prepared cake pan.
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Start around the edges and fill in the center.
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Bake until the pastry is cooked through and golden brown, 35 to 40 minutes.
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Meanwhile, for the glaze: In a small pot, add the butter and melt over low heat.
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Add the vanilla extract and lemon juice and begin whisking in the powdered sugar in 1/4 cup increments.
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Continue adding and whisking between additions until the glaze thickens.
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Season with a pinch of salt, then remove from the heat.
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Remove the buns from the oven and pour the glaze over the top.
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Let rest about 5 minutes before serving.
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Serve warm.
