In a large mixing bowl combine the yogurt, lemon juice, red chili powder (or cayenne), red pepper flakes, garlic paste (or minced garlic), ginger paste (or ground ginger), kosher salt, smoked paprika, and tandoori seasoning; mix until smooth.
Pat the chicken pieces dry with paper towels and make 1-inch apart, 1/2-inch deep slits across the top of each piece.
Add the chicken to the yogurt mixture and rub the marinade all over each piece, working the marinade into the slits; set the bowl aside and let the chicken marinate on the countertop for 30 minutes.
Heat the butter and olive oil in a large cast iron or heavy skillet over medium-high heat until hot.
Add chicken pieces to the hot skillet without crowding and sear the first side 1½–2 minutes until golden; flip and cook about 2 minutes, repeating and turning as needed until all sides are browned and the chicken is cooked through (about 10–12 minutes total depending on piece size).
Check doneness with a meat thermometer inserted into the thickest part: target 160°F for white meat and 165°F for dark meat; transfer finished pieces to a large heatproof bowl as they come out of the pan.
Prepare a small 4-inch heatproof bowl or fold aluminum foil into a 4-inch bowl and nestle it among the stacked chicken pieces.
Using heatproof tongs, hold a smoking wood chip or chunk of untreated charcoal over a gas burner or lighter until it starts to smoke; place the smoking chip/coal into the small bowl, drizzle a few drops of oil over it, then quickly cover the whole skillet or bowl with a large lid to trap the smoke for 3 minutes.
After 3 minutes, remove the lid and the smoking chip/coal and discard the small bowl; transfer the smoked tandoori chicken to a serving platter and serve immediately with thinly sliced red onion, lemon wedges, and chopped cilantro.
