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1
Bring water, sugar, rose hips, and cardamom pods to a simmer in a small heavy saucepan over medium-low heat, stirring until sugar has dissolved, then gently simmer, uncovered, until rose hips are softened, about 30 minutes. Remove from heat and stir in rose water and lemon juice.
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2
Whisk together flour, kosher salt, and spices in a small bowl.
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3
Bring water to a boil with butter and sugar in a 3-quart heavy saucepan, stirring until butter has melted. Add flour mixture all at once and cook over medium heat, stirring vigorously with a wooden spoon, until mixture pulls away from side of pan, about 1 minute, then cook, stirring constantly, 1 minute more. Cool 5 minutes.
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4
Add eggs 1 at a time, beating well with a wooden spoon after each addition. (Dough will appear to separate at first but will become smooth.)
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5
Heat 2 inches oil to 350u00b0F in a wide 5-quart heavy pot over medium-high heat.
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6
Divide dough into 12 portions. With wet hands, form each portion into a 2-inch ball (dough will be sticky). Slightly flatten one ball in a wet palm, then make a 1-inch hole in center with fingers and add to hot oil. Quickly repeat with 5 more balls and fry, turning occasionally, until golden-brown and just cooked through (cut one open to test), about 8 minutes. Transfer with a slotted spoon to paper towels to drain. Return oil to 350u00b0F and repeat with remaining dough.
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7
Reheat syrup (if necessary), then dip each doughnut in syrup, turning to coat, and transfer to a platter. Drizzle doughnuts with some of remaining syrup and serve warm.
