In a bowl, combine the chicken with lemon juice, Kashmiri chili powder, sweet paprika, and salt. Stir in the yogurt, ginger, garlic, garam masala, and vegetable oil until evenly coated. Cover and refrigerate for at least 1 hour, preferably 4-6 hours or overnight. Remove from the fridge 15 minutes before cooking.
Preheat the oven to 480°F (250°C) using the broiler (grill) setting if available. Arrange the marinated chicken on a wire rack placed over a baking sheet lined with parchment paper. Bake for 12-15 minutes, flipping halfway, until slightly charred. Set aside.
In a deep pan over medium heat, dry toast the cardamom and cinnamon for 30 seconds, stirring occasionally.
Add the butter to the pan and let it melt. Stir in the grated ginger and garlic, cooking for 1 minute while stirring constantly.
Add the tomato paste and cook for 1 minute, stirring frequently until it darkens slightly.
Pour in the tomato purée, cashews, Kashmiri chili powder, sweet paprika, sugar, and salt. Add ½ cup (120 ml) water to thin out the sauce. If the sauce appears too thick while simmering, add up to ¼ cup (60 ml) more water, one tablespoon at a time. Simmer on low heat for 10-15 minutes, stirring occasionally, until the cashews soften and the sauce slightly thickens.
Remove the cinnamon stick, then blend the sauce with an immersion blender until smooth.
Return the blended sauce to low heat and stir in nutmeg and lemon juice or apple cider vinegar for a balanced depth of flavor. Add the baked chicken and let it simmer for 10 minutes, stirring occasionally to coat it in rich sauce. Finally, stir in the heavy cream until fully incorporated for a smooth, velvety finish.
Drizzle with yogurt, sprinkle with kasoori methi or dried mint, and serve with naan or roti, red onion slices, green chilies, and lime wedges.