Stir together chicken, 1 tablespoon lemon juice, 1 teaspoon ginger, 1 teaspoon garlic, 1 teaspoon smoked paprika, 1 teaspoon cumin, 1 teaspoon salt, and ½ teaspoon garam masala in a large bowl until evenly coated.

Melt 2 tablespoons butter in a large broiler-safe skillet or braiser over medium-high. Add chicken in an even layer, and cook, undisturbed, until browned, about 4 minutes. Turn chicken, and continue cooking until evenly browned and cooked through, about 4 minutes. Transfer chicken to a plate. Do not wipe skillet clean.

Melt remaining 1 tablespoon butter in the same skillet over medium-low. Add remaining 1 teaspoon each ginger and garlic; cook, stirring constantly, until fragrant, about 30 seconds. Stir in cayenne pepper (if desired), remaining ½ teaspoon smoked paprika, remaining ½ teaspoon cumin, remaining ½ teaspoon salt, and remaining ¼ teaspoon garam masala. Cook, stirring constantly, until fragrant, about 30 seconds. Stir in tomato paste, and cook, stirring constantly, until tomato paste darkens slightly, about 1 minute.

Stir in orzo, chicken stock, and heavy cream. Bring to a boil over medium-high. Reduce heat to medium, cover and simmer, stirring occasionally, until orzo begins to soften, 10 to 12 minutes. Uncover, and continue cooking, stirring occasionally, until orzo is almost tender, 2 to 3 minutes.

Stir in chopped cilantro, cooked chicken and any accumulated juices, and remaining 1 tablespoon lemon juice. Cook, stirring occasionally, until orzo is tender and sauce is slightly thickened, about 2 minutes.

Preheat oven to broil with rack about 6 inches from heat source. Remove skillet from heat. Top evenly with cheeses. Broil until cheese is melted and browned in spots, 2 to 3 minutes. Garnish with additional chopped cilantro. Serve with lemon wedges.