In a large saucepan, combine the leek greens, chicken broth, rice mix, 2 tbsp. butter and 1/2 tsp. salt. Bring to a boil, lower the heat, cover and simmer until the liquid is mostly absorbed and the rice is cooked, about 50 minutes. Discard the leek greens and scrape the rice mixture (including any liquid) into a large bowl.
Preheat the oven to 350 degrees . Grease a 9-by- 13-inch baking dish. Spread the almonds on a baking sheet and bake until toasted, about 8 minutes. Add to the rice.
Meanwhile, chop the leek whites. In a large skillet, melt 2 tbsp. butter over medium heat. Add the leek whites and cook until tender, about 5 minutes. Transfer to the rice. Melt the remaining 3 tbsp. butter in the skillet and add the mushrooms. Cook, stirring occasionally, until nicely browned, about 12 minutes. Scrape into the bowl with the rice and add the currants, parsley, lemon zest, allspice, 1 tsp. salt and 1/2 tsp. pepper. Mix well and transfer to the prepared baking dish, patting the stuffing down. Cover with greased foil and bake until hot, about 45 minutes. Uncover and bake until lightly browned, about 15 minutes.