Using a mortar and pestle, combine the garlic, chile, salt, coriander, mustard seeds, and turmeric, and grind into a paste.
For the curry:
Heat 2 tablespoons of the oil in a large ovenproof casserole or heavy-bottomed saucepan. Season the chicken with salt, and black pepper, and brown the pieces on all sides. Remove the chicken from the pan, and set aside. Add the remaining oil, and cook the squash, onions, eggplants, and potatoes.
Once the vegetables begin to soften and brown, sprinkle in the spice mix, and cook, stirring continuously, for 4 minutes to release the fragrance of the spices. Return the chicken to the casserole dish, and add the bay leaves, coconut milk, chicken stock, and tamarind paste.
Bring the ingredients to a boil, then reduce the heat to a simmer, and cover. Cook until the chicken is tender and cooked through, about 40 minutes. About 5 minutes before serving, stir in the mango, papaya, lime juice, and rum, if using. Stir the mixture to incorporate, then cover, and cook until the fruit is hot. Adjust the salt, and pepper, if necessary, and serve with some boiled rice.
If the pan isn't big enough, cook the onion and eggplant first, then add the squash and potato once the other vegetables start to brown.
*Can be found at specialty Asian markets.