Pulse ginger and garlic in a food processor until finely chopped. Add onion and pulse again until finely chopped.

Toss chicken with 1 1/2 tsp. salt, 1/2 tsp. pepper, and 1 tsp. garam masala in a medium bowl.

Heat oil over high in a large skillet (at least 12 in diameter). Add chicken and cook, tossing occasionally, until lightly browned and cooked through, about 5 minutes. Transfer chicken to a clean medium bowl.

Heat same skillet over medium-high and add butter, chopped onion mixture, 1/2 tsp. salt, and 1/4 tsp. pepper. Cook, stirring constantly, until onion is softened and translucent, about 3 minutes. Add tomato paste, turmeric, cayenne, and remaining 1 1/2 tsp. garam masala and cook, stirring constantly, about 30 seconds. Add tomatoes and cook, stirring occasionally, until hot, about 2 minutes. Return chicken to pan, add peas, and cook, stirring occasionally, until warmed through, about 1 minute more.

Remove from heat and stir in yogurt and lemon juice. Season with salt and pepper. Divide among 4 plates, top with cilantro, and serve with naan.