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Rehydrate dried shitake mushrooms by placing them in a bowl of hot water for about 30 minutes, until softened. Cut stems off.
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Place onion and ginger on baking sheet and bake at 425 degrees for about 20 minutes or until slightly softened and onion skin is charred. Remove onion skin and ginger skin.
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To prepare lemongrass, cut off <g class="gr_ gr_1097 gr-alert gr_spell gr_disable_anim_appear ContextualSpelling" id="1097" data-gr-id="1097">stalky</g> top part, leaving bottom 1/3. Trim about 1/2" off <g class="gr_ gr_1101 gr-alert gr_gramm gr_run_anim Grammar only-ins doubleReplace replaceWithoutSep" id="1101" data-gr-id="1101">bottom</g>, and remove outer leaves until <g class="gr_ gr_1102 gr-alert gr_gramm gr_run_anim Grammar only-ins replaceWithoutSep" id="1102" data-gr-id="1102">tender</g> bulb is exposed. Crush bulb with <g class="gr_ gr_1103 gr-alert gr_gramm gr_run_anim Grammar only-ins doubleReplace replaceWithoutSep" id="1103" data-gr-id="1103">flat</g> side of a large knife.
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Lightly toast star anise and cloves in a small skillet.
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Combine broth, water (note: if using homemade vegetable broth, use 2 cups more broth instead of water; boxed vegetable broth tends to be too strong), rehydrated shitake mushrooms, onion, ginger, lemongrass, star anise, cloves, cinnamon stick, palm sugar and soy sauce in a saucepan. Bring to boil, then lower heat and simmer 30 minutes. Strain broth, reserving shitake mushrooms. Slice shitake mushrooms and save for topping.