Lamb and Broccoli Stew

Whisk sugar, 3/4 cup salt, and 10 cupswater in a large bowl until salt and sugardissolve.

Add lamb, cover, and chill for atleast 12 hours and up to 2 days.

Heat oil in a large heavy pot over medium-highheat.

Add onions, garlic, rosemarysprig, thyme sprig, and bay leaf. Cook,stirring often, until onions are golden brownand soft, 10-15 minutes.

Remove pot fromheat and add wine, stirring and scrapingup any browned bits from bottom of pan.Return pot to heat and simmer until wineis reduced by half, about 3 minutes.

Remove lamb shoulder from brine; add topot, along with broth. Bring to a boil. Reduceheat; simmer gently, partially covered andskimming fat occasionally, until lamb is fork-tender,5-6 hours.

Transfer lamb to a platter and removebones.

Cut or shred meat into bite-sizepieces. If needed, boil cooking liquid in potuntil reduced to 6 cups, 15-30 minutes.Season sauce with salt, if needed. Returnlamb to pot. DO AHEAD: Lamb can beprepared 3 days ahead.

Let cool slightly,then chill until cold. Cover and keep chilled.Discard fat and reheat before serving.

Place eggs in a small saucepan and add water tocover by 1". Bring to a boil and remove fromheat. Cover and let sit for 3 minutes.

Transfer eggs to a bowl of ice water andlet cool completely. Peel.

Combine eggs, garlic, 3 tablespoons lemonjuice, and 1/2 teaspoons salt in a blender. With themotor running, gradually add oil, blendinguntil a creamy sauce forms. Season garlicemulsion with salt and more lemon juice, ifdesired.

Cook broccoli in a large pot of boilingsalted water until crisp-tender, about4 minutes.

Drain; rinse under cold water.

Divide stew among bowls and garnishwith broccoli, parsley, tarragon, and garlicemulsion.