In a large bowl, whisk the yogurt, lemon juice, garlic (4 cloves, grated), ginger (1 tbsp), Kashmiri red chili powder (2 tsp), garam masala (2 tsp), ground cumin, turmeric, kosher salt (1.25 tsp), and neutral oil (1 tbsp). Add the chicken pieces and coat well; cover and marinate 30 minutes (or up to overnight).
Heat the broiler to high and set a rack in the upper third. Arrange the marinated chicken on a foil-lined sheet with a wire rack. Broil 10–15 minutes, turning once, until lightly charred at the edges and cooked through (165°F). Reserve any pan juices.
In a wide saucepan over medium heat, melt 4 tablespoons unsalted butter with the neutral oil (1 tbsp) until foaming.
Add the green cardamom pods, cinnamon stick, and bay leaf; stir until fragrant, 30–60 seconds.
Add the garlic (3 cloves, chopped) and ginger (1 tsp); sauté until the raw aroma fades, about 1 minute.
Sprinkle in the Kashmiri red chili powder (1 tsp) and ground coriander; stir 10–15 seconds to bloom the spices.
Add the canned whole peeled tomatoes with their juices and kosher salt (1 tsp). Bring to a gentle simmer.
Simmer uncovered, stirring occasionally, 15–20 minutes until the tomatoes break down, the sauce thickens slightly, and fat begins to separate.
Remove and discard the cinnamon stick, bay leaf, and any cardamom husks. Blend the sauce until perfectly smooth using an immersion blender (or cool slightly and blend, then return to the pan). For extra silkiness, strain through a fine sieve back into the pan.
Stir in the heavy cream, sugar, garam masala (1 tsp), and dried fenugreek leaves (crushed). Simmer 5 minutes, stirring often, until slightly thickened and glossy.
Add the broiled chicken and any reserved pan juices; simmer 5–8 minutes, stirring to coat, until the chicken is tender and the sauce clings.
Stir in the remaining 2 tablespoons unsalted butter to finish. Adjust salt to taste and remove from heat.
Let rest 5 minutes to mellow the spices. Garnish with cilantro leaves and serve hot with basmati rice or naan.