Use a fork to prick the chicken breasts all over on both sides. Cover with plastic wrap. Using the smooth side of a meat mallet or a rolling pin, beat the chicken until the breasts are an even ½ to ¾ inch thickness.
In a small bowl, whisk together the yogurt, 1 tbsp peanut oil, lime juice, and garlic. Add the pounded chicken, and rub the marinade over the meat. Set the chicken aside while you make the sauce.
In a small bowl, whisk together the coriander, cumin, cardamom, nutmeg, paprika, cayenne, and grated ginger.
In a heavy wide 4-quart pot or sauté pan over moderately high heat, melt the butter. Add the onion and sauté, stirring occasionally, until light brown and caramelized, about 5 minutes.Reduce the heat to moderate, then stir in the spice and ginger mixture.
Add the tomato puree, water, heavy cream, and salt, and bring the sauce to a boil. Reduce the heat to gently simmer the sauce, uncovered, until thickened slightly, about 10 minutes. The sauce can be prepared ahead and refrigerated in an airtight container, up to 3 days.
While sauce simmers, cook the chicken
Heat a heavy 11-12 inch griddle or skillet over moderately high heat until very hot and add ½ tablespoon of peanut oil to each batch. Working in two batches, cook the chicken breasts, turning them a few times until just cooked through and browned well on both sides, 6 to 8 minutes total.
When all the chicken is cooked, cut it into 1½ inch pieces. Add the chicken to the simmering sauce and continue to gently simmer it, stirring occasionally, for 5 minutes. Remove the pan from the heat, stir in the black pepper and chopped cilantro, and season with salt.
Transfer the chicken to a serving dish and garnish with additional cilantro sprigs.
If you prefer to make the sauce with fresh tomatoes, chop 1 pound fresh tomatoes and purée them, including the skins and seeds, in a blender with 1 tablespoon tomato paste and 3/4 teaspoon sugar. When using fresh tomatoes, omit the 3/4 cup water from the recipe.
If you are really short on time, substitute the meat from a rotisserie chicken.