Heat oil in a medium skillet over medium-high heat. Add chicken and cook until golden brown, 3 to 4 minutes per side. Transfer to a 6-quart slow cooker.
Add onion to the pan and cook, stirring occasionally, until translucent, about 4 minutes. Stir in ginger, garlic, garam masala and cardamom; cook, stirring constantly, until fragrant, about 1 minute.
Transfer the mixture to the slow cooker. Stir in coconut milk, broth and tomato paste. Cover and cook on Low until the chicken is tender and cooked through, 7 to 8 hours.
About 40 minutes before serving, combine water and rice in a medium saucepan and bring to a boil over medium-high heat. Stir and cover; reduce heat to low and simmer until the rice is tender, about 30 minutes. Remove from heat and let stand, covered, for 10 minutes. Fluff with a fork.
Stir salt into the chicken mixture. Serve the chicken and sauce over the rice. Garnish with lime wedges and scallions, if desired.
Equipment: 6-qt. slow cooker
4 lean protein, 2 starch, 1 1/2 fat, 1 vegetable