Butterfly each chicken breast into two equal pieces by cutting through them horizontally.
Whisk together yogurt, 2 tbsp peanut oil, lime juice and garlic. Add chicken to this marinade and completely coat. Marinate for at least one hour.
Combine white cabbage, red cabbage, cilantro and lime juice to make slaw.
Whisk together the coriander, cumin, cardamom, nutmeg, paprika, cayenne and ginger in a small bowl. In a sauté pan over medium high heat, melt the butter and caramelize onions to a light brown color.
Reduce heat to medium, then stir in the spice mixture. Add tomato puree, water, heavy cream and salt, and bring the sauce to a boil. Reduce the heat to a gentle simmer and allow sauce to thicken slightly, about 10 minutes.
Oil and heat skillet to medium high heat until hot. Add 1 tbsp peanut oil. Working in batches, cook chicken breasts, turning them a few times and lowering the heat if the chicken chars too quickly, until browned well on both sides and cooked through. Should take 6 to 8 minutes total. Let chicken cool, slice thinly.
Assemble sliders with chicken on bottom bun, topped with slaw and tikka masala sauce. Serve with extra sauce on the side.