Pulse the ginger, garlic, garam masala and 1/4 teaspoon each cayenne and salt in a food processor to make a paste. Toss the cauliflower, 1 tablespoon of the spice paste, 1 tablespoon water and a pinch of salt in a microwave-safe bowl; set aside. Add the tomato paste to the remaining spice paste; pulse, then transfer 1 tablespoon to a bowl. Add 1/2 cup yogurt, a pinch of salt and the chicken; toss to coat.
Heat the olive oil in a skillet over medium-high heat. Add the remaining tomato-spice mixture and cook, stirring, 3 minutes. Add the tomatoes, 1 1/4 cups water and 1/2 teaspoon salt; bring to a simmer and cook until thickened, 15 to 20 minutes.
Meanwhile, preheat the broiler. Put the chicken on a foil-lined baking sheet and broil until almost cooked through, 5 to 6 minutes per side. Microwave the cauliflower, 10 to 12 minutes. Toss with the cilantro.
Whisk the remaining 1/4 cup yogurt into the skillet. Add the chicken; simmer until cooked through, 4 minutes. Serve with the cauliflower.