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1
Bring 8 quarts water and vinegar to boil in 10- to 12-quart pot.
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2
Add 2 lobsters headfirst and cook until shells turn bright red and lobsters are just cooked through, about 11 minutes.
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3
Using tongs, remove lobsters from water.
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4
Repeat with remaining 2 lobsters.
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5
Twist claws and tails off lobsters.
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6
Crack claws and remove meat.
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7
Using kitchen shears or heavy large knife, cut lobster tails lengthwise in half; remove tail meat.
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8
Cut meat into large bite-size pieces.
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9
Place in medium bowl; cover and refrigerate.
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10
Reserve claw and tail shells.
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11
Using kitchen shears, cut away lobster gills.
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12
Rinse shells under cold water.
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13
Place in large bowl.
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14
Pour cold water over and soak 10 minutes.
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15
Drain; rinse well.
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16
Heat 1/4 cup oil in large pot over medium heat.
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17
Add lobster shells, carrots, and next 4 ingredients.
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18
Cook until vegetables begin to soften, stirring occasionally, about 15 minutes.
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19
Add 4 quarts water and simmer 45 minutes, stirring occasionally.
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20
Strain lobster broth into large bowl, pressing on solids.
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21
Strain broth again through fine strainer into same pot.
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22
Boil over medium-high heat until broth is reduced to 2 cups, about 1 hour.
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23
(Can be made 1 day ahead.
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24
Cool slightly; chill broth and lobster meat separately.)
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25
Bring 1 quart water to boil in tea kettle.
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26
Place 2 cups rosemary in each of 4 large bowls; place on table.
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27
Melt 2 tablespoons butter with 1/4 cup oil in large skillet over medium-high heat.
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28
Add mushrooms, thyme, and garlic and saute until mushrooms are tender, about 6 minutes; discard thyme and garlic.
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29
Add lobster and 1/2 cup butter to skillet and heat through, about 3 minutes.
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30
Meanwhile, bring lobster broth to simmer in small saucepan.
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31
Pour hot lobster broth into blender; add 1 cup butter.
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32
Blend until butter is melted and mixture is frothy, about 30 seconds.
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33
Divide lobster mixture among 4 shallow bowls.
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34
Pour butter sauce and foam over lobster mixture and serve.
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35
Pour 1 cup boiling water into each bowl of rosemary to create vapor.
