Step 1: Preheat oven to 350F.
Step 2: Coat garlic lightly with vegetable oil and wrap in foil. Bake garlic 30 minutes, or until soft.
Step 3: In a dry small heavy skillet toast coriander and cumin seeds over moderately high heat, stirring, until fragrant and several shades darker.
Step 4: In an electric coffee/spice grinder grind seeds to powder.
Step 5: Chop onions and in a 6-quart heavy kettle cook in 2 tablespoons oil over moderate heat, stirring, until softened.
Step 6: Reserve about one third onions in a small bowl.
Step 7: Wearing rubber gloves, slice jalapeño and chop roasted poblanos (abut 1 cup).
Step 8: Remove kernels from ears of corn (about 2 cups), reserving cobs.
Step 9: To onions in kettle add jalapeño and 1 cup corn kernels and cook over moderate heat, stirring, 2 minutes.
Step 10: Add ground spices, 1/2 cup poblanos, and salt and pepper to taste and cook, stirring, 2 minutes. Cut reserved corn cobs into thirds and add with broth to corn mixture.
Step 11: Simmer soup, uncovered, 30 minutes.
Step 12: In a small heavy skillet sauté remaining kernels in remaining teaspoon oil over moderately high heat, stirring, just until tender.
Step 13: Discard corn cobs from soup.
Step 14: Squeeze garlic pulp from skins and stir with cream into soup.
Step 15: Pour soup through a sieve into a bowl and in a blender purée solids with just enough liquid to make smooth.
Step 16: Tie long coriander sprigs in a bunch with kitchen string.
Step 17: Transfer purée and remaining liquid to kettle with tied coriander and lime juice and cook over moderate heat, stirring occasionally, just until heated through.
Step 18: Chop roasted bell pepper.
Step 19: To soup add bell pepper, remaining poblanos, reserved onions, and sautéed corn and cook over moderate heat, stirring, until heated through.
Step 20: Discard tied coriander.
Step 21: Serve soup garnished with coriander.
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