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Heat 1 tablespoon of the oil in a large, heavy skillet. Add the chopped onion and shallot and cook under medium-low heat for about 5 minutes, until the pieces start to become transparent.
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Add the butter, ginger garlic paste, bay leaf, garam masala, chili powder, cumin, coriander, cayenne, and lemon juice. Cook for another 1-2 minutes, stirring to mix all the spices. Add the tomato sauce and cook, stirring frequently for 2-3 minutes more.
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Stir in the ground cashews, dairy (half and half or cream/milk and yogurt), and salt. Simmer the sauce under a low heat for 10 minutes, stirring frequently. Cool the sauce down slightly and blend, either in a blender or with an immersion blender in a tall glass or bowl. Set aside.
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Either clean the skillet or use another one. Add a tablespoon of oil (the second of three) and sauté half the chicken cubes on medium-high heat. Leave enough room around each cube so that they do not touch and turn them to brown on each side. Once those cubes are seared on all sides, remove them from the skillet to a plate, add the third tablespoon of oil, and sauté the rest of the chicken cubes the same way.
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Once all the chicken cubes are finished cooking, add the sauce back into the skillet and simmer the sauce on a low heat for 20 minutes. If you prefer the sauce thinner, add in small amounts of chicken broth until you get the consistency you want.