Peel and grate the ginger and garlic into a prep bowl. Use a masher, fork, or back end of a spoon to combine into a paste.
Remove the tops off the peppers (saving), discard the stem, membranes and seeds. Dice up the remaining part of the top. On the stovetop bring a couple quarts of water to a boil, enough to cover and parboil the peppers. Boil for 3 - 4 minutes. Remove from heat and set aside.
While that is going on, heat the oil on medium heat in a large skillet. Add in diced pepper tops and onions, cook until onions start to take on color, stirring occasionally, about 10 minutes. Add garlic/ginger paste, chili peppers, and mustard. Cook until onions start to take on a reddish brown color, again stirring occasionally but a little more frequently now (may have to deglaze pan). About 10 more minutes here.
Add the coriander, cumin, and garam masala, stirring and until fragrant. Add in the lamb, mint, and turmeric and cook until just browned.
Stir in the fire roasted tomatoes (with liquid). Allow liquid to reduce. Stir in half the cilantro.
Fill the peppers, with mixture, Bake for 30 minutes at 350°, covered. Remove foil or covering, sprinkle cheese on top. Cook uncovered for another 7 - 10 minutes or until cheese melts an begins to take on color. Remove, top with remaining cilantro for garnish and serve.