Place chicken thighs on cutting board. Use sharp knife to cut chicken into small, evenly-sized pieces, then spread pieces out in single layer. Liberally sprinkle salt over chicken pieces, then flip chicken over and salt other side. Set cutting board aside.
Heat wok over medium-high heat. Once skillet is very hot, add peanut oil and swirl wok to distribute oil evenly. Continue heating wok until oil is hot and shimmery.
When oil is ready, add half of chicken pieces to wok. Cook chicken, stirring frequently, approximately 4 minutes or until lightly browned.
Transfer browned chicken to large plate and set aside, then repeat process with remaining uncooked chicken.
Once all chicken has been cooked, discard remaining oil. Return wok to stovetop and reduce heat to medium-low.
Add butter to wok and let melt completely, swirling wok occasionally to distribute melted butter evenly.
When butter is completely melted (but not browned or bubbling), add garam masala, sweet paprika, coriander, ginger, chili powder, cinnamon stick, and bruised cardamom pods to wok. Simmer spices, stirring constantly, approximately 1 minute or until just fragrant.
Return chicken pieces to wok and stir to coat chicken in spices.
Add tomato sauce and sugar to wok. Stir well to fully incorporate ingredients, then simmer mixture 10 to 15 minutes, until chicken reaches internal temperature of 160° to 163° Fahrenheit.
Once chicken reaches desired temperature, remove wok from heat. Let mixture cool slightly, then add yogurt, heavy cream, and lemon juice. Gently stir until ingredients are fully incorporated into tomato sauce.
Return wok to heat. Simmer 5 minutes or until sauce has thickened and chicken is cooked through. Taste sauce and add salt if desired.
Divide butter chicken into preferred portions and plate with basmati rice and fresh naan. Garnish chicken with chopped cilantro if desired and serve immediately.