Preheat oven to 375°. Slice caps from bell peppers 1/2 to 1 in. from stems and save caps. Pull out seeds and membranes from peppers and discard, or scrape out with a small spoon. If needed, cut a paper-thin slice from bottoms of peppers (without cutting holes in them) to help peppers stand flat.
Set aside 1 tsp. garlic. Put remaining garlic, the onion, and 2 tbsp. oil in a 12-in. cast-iron skillet or other ovenproof frying pan and cook over medium-high heat, stirring occasionally, until softened, 4 to 5 minutes. Stir in 1 1/4 tsp. salt, the black pepper, allspice, cinnamon, and rice. Cook, stirring, until rice is opaque, 2 to 3 minutes. Add 1 cup water and cook at a rapid simmer, stirring occasionally, until liquid evaporates, 4 to 5 minutes. Add 1/2 cup water and repeat cooking until liquid evaporates, about 3 minutes. Add tomato and cook until it's softened, about 3 minutes; mixture should be somewhat soupy.
Scrape rice mixture into a large bowl. Stir in lamb, pine nuts, mint, dill, and parsley until lamb is evenly distributed. Wipe skillet clean.
Spoon lamb mixture into peppers, pushing down into cavities, to about 1/4 in. from tops*, and set peppers upright in skillet. Set pepper caps in place. Drizzle peppers with 2 tbsp. oil. Pour 1 cup water into bottom of skillet and add bay leaves.
Bake peppers, basting every 20 minutes or so with pan juices, until peppers are well browned, about 1 hour and 10 minutes; if some brown faster than others, tent with foil. Meanwhile, in a small bowl, combine yogurt and remaining 1 tsp. garlic and 1/2 tsp. salt; chill until used.
Spoon pan juices over peppers and scatter more mint on top. Swirl remaining 1 tbsp. oil into yogurt sauce and serve with peppers.