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Preheat the oven to 350°F Position a rack in the center of the oven. Butter a 9-by-13-inch metal baking pan.
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Make the crumb topping: Spread the pecans on a rimmed baking sheet and toast for 8 minutes, until browned. Let cool, then coarsely chop the nuts.
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In a medium bowl, stir the melted butter with both sugars, the cardamom and salt.
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Add the flour and stir until clumpy.
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Stir in the chopped nuts.
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Make the cake: In a large bowl, whisk the flour with the sugar, baking powder and salt.
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In a medium bowl, whisk the eggs with the milk, melted butter and vanilla.
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Add the egg mixture to the dry ingredients and stir until just combined.
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Scrape the batter into the prepared baking pan, smoothing the surface.
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Scatter the crumbs in large clumps over the cake; the crumb layer will be quite deep.
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Bake for about 55 minutes, until the crumbs are golden and firm and a tester inserted in the center of the cake comes out clean. If the crumbs brown before the cake is done, cover the cake loosely with foil.
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Transfer to a rack to cool.
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Make the glaze: In a bowl, whisk all of the glaze ingredients together. Drizzle the glaze over the cake; let cool slightly.
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Serve warm or at room temperature.
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The cake can be kept covered at room temperature for up to 3 days.