In a small bowl, combine the salt, pepper, cumin, smoked paprika, turmeric, coriander, cardamom, dry mustard, cayenne, and allspice. Stir to combine.
In a large bowl, add the cubed chicken thighs, 2 tablespoons of yogurt, 4 cloves of minced garlic, the ginger, and half of the spice mixture. Toss the chicken until it is fully coated. Cover the bowl with plastic wrap, and marinate in the fridge for 2 hours or overnight.
Make the naan bowls: In a liquid measuring cup, combine the warm water, sugar, and yeast. Set aside to bloom for 10 minutes.
In the meantime, mix the flour, baking powder, baking soda, and salt together in a large bowl.
To the yeast mixture, add the yogurt and milk. Stir until smooth, then pour into the dry ingredients. Stir to combine, then dump the dough out onto a floured surface and knead with your hands until it forms a smooth, soft ball, about 2 minutes.
Place the dough in a clean large bowl greased with olive oil and cover with a clean kitchen towel or plastic wrap. Let rise at room temperature until doubled in size, about 2 hours.
Heat the olive oil in a large Dutch oven over medium-high heat. Working in batches to avoid overcrowding the pot, cook the marinated chicken on all sides until cooked through and browned, about 20 minutes. Drizzle in more oil, as needed, to prevent the meat from sticking to the bottom of the pot. Transfer the browned meat to a plate as it finishes cooking and set aside.
Add the carrots, onion, potatoes, remaining 5 cloves of minced garlic, and reserved spice mixture, Stir and cook until the vegetables brown slightly and start to soften, 15 minutes.
Stir in the tomato paste and cook until aromatic, about 3 minutes.
Add the crushed tomatoes and chicken broth. Stir to combine. Bring to a simmer.
Add the chicken, stir, and return to a simmer. Cover and cook for 30 minutes, or until the potatoes are tender and the chicken is cooked through.
Stir in the remaining 3 tablespoons of yogurt, then cover and keep warm.
Once the naan dough has risen, dump onto a floured surface, and divide into 6 equal portions. Roll each portion into a ¼-inch (1 /2 cm) thick circle, approximately 10 inches (25 cm) in diameter.
Heat a large cast-iron skillet over medium-high heat. Place a disc of naan dough in the skillet. Cook for about 2 minutes, until the dough puffs up, then flip and cook on the other side until browned, 1 minute. Transfer the naan to a medium bowl and place another bowl on top. Repeat with the rest of the naan dough, stacking bowls between each round. As the naan cools, they will retain the bowl shape.
Brush the naan bowls with warm melted butter.
Fill the naan bowls with the chicken curry and rice. Serve with yogurt, cilantro, and lime wedges.