Preheat oven to 180C. Scatter almonds on an oven tray and roast, stirring occasionally, until golden (5-7 minutes). Cool, coarsely chop and transfer to a bowl.
Dry-roast whole spices until fragrant (20-30 seconds). Cool slightly, finely grind in a mortar and pestle, then combine with almonds, dates, preserved lemon rind, mint, parsley, garlic, paprika and cinnamon, season to taste and set aside.
Open lamb shoulder out, press herb mixture over one half, fold other half over, tie with kitchen string and set aside.
Place carrots in the base of a roasting pan, place lamb on top, drizzle with oil, season to taste and roast, basting occasionally, until just cooked through (1½-1¾ hours). Cover with foil and set aside to rest (10 minutes).
For mint yoghurt sauce, combine yoghurt, mint and lemon juice in a bowl, season to taste, stir to combine, refrigerate until chilled.
Meanwhile, for mint burghul, cook burghul in a saucepan of boiling water over high heat until tender (5-10 minutes), drain and scatter over a tray to cool and dry. Transfer to a bowl, add remaining ingredients and season to taste. Serve with lamb, roast carrots and mint sauce.