Combine the chicken, 1 tbsp butter, 2 tbsp plain yogurt (marinade portion), 1/2 tsp ground cumin, 1/2 tsp ground cayenne, 1/2 tsp ground garam masala, 1/2 tsp minced ginger, 1/4 tsp salt, 1/4 tsp ground black pepper, 1 tbsp lemon juice, and a pinch of cinnamon in a mixing bowl; mix until the chicken is evenly coated.
Cover and refrigerate the marinated chicken for at least 1 hour.
Preheat the oven grill to 450°F (232°C). Line a baking pan with foil and arrange the marinated chicken in a single layer, discarding excess marinade; grill for 6–7 minutes, flipping once, until cooked through.
While the chicken cooks, combine the sauce ingredients: 4 oz tomato sauce, 2 tbsp plain yogurt (sauce portion), 2 tbsp heavy cream, 1/2 tsp cumin, 1/2 tsp paprika, and 1/2 tsp garam masala in a bowl and set aside.
Heat a small saucepan over medium heat and melt the remaining butter; sauté the minced garlic and minced jalapeño until fragrant, about 1 minute, then add the spice mix and cook 1–2 minutes more. Remove and discard the jalapeño.
Add the prepared tikka masala sauce to the saucepan, season with salt to taste, and simmer until slightly thickened, about 2 minutes. Turn off the heat and stir in the grilled chicken to coat it in the sauce.
Preheat the oven to 450°F (232°C). Place the pizza crust on a pizza pan and lightly brush with olive oil.
Spread the chicken tikka masala sauce evenly over the crust, sprinkle with 1/2 cup mozzarella, arrange the sauced chicken on top, add the thinly sliced onions and chopped cilantro, then finish with the remaining mozzarella.
Lower the oven temperature to 425°F (218°C) and bake the pizza for 8–10 minutes, or until the crust is golden and the cheese is melted.
Remove the pizza from the oven, garnish with the remaining chopped cilantro, slice, and serve.