Gather the ingredients.
Make a spice mix by combining garam masala, tandoori masala, curry powder, cumin, cardamom, cayenne, salt, and black pepper in a small bowl; set aside.
Place chicken in a large bowl and add 1/2 of the spice mixture; turn to coat evenly.
Melt 1 tablespoon butter in a large skillet over medium heat. Add chicken; cook and stir until lightly browned, about 10 minutes. Remove from heat.
Melt remaining 2 tablespoons butter in a large saucepan over medium heat. Add onion; cook and stir until soft and translucent, about 5 minutes. Stir in remainder of the spice mixture, garlic, lemon juice, and ginger; cook and stir until combined, about 1 minute.
Stir tomato puree into onion mixture and cook, stirring frequently, about 2 minutes. Pour in half-and-half and yogurt. Reduce heat to low and simmer sauce, stirring frequently, about 10 minutes. Remove from heat.
Blend cashews in a blender until finely ground. Add sauce to the blender; puree until smooth.
Pour blended sauce over chicken in the skillet. Simmer until thickened, 10 to 15 minutes. Garnish with cilantro.
