Pat chicken dry with paper towels; season both sides with salt and garam masala. In a large skillet over medium heat, heat oil, swirling pan to coat. Arrange half of chicken in skillet skin side down and cook, undisturbed, until skin is crisp and deep golden brown, 7 to 8 minutes. Turn chicken and cook, undisturbed, until an instant-read thermometer inserted into thickest part registers 165°, 7 to 8 minutes. Transfer chicken to a plate, wipe any burnt bits in pan, and repeat with remaining chicken.
Reduce heat to medium-low. Cook lemongrass (if using), ginger, and garlic, stirring, until fragrant, about 1 minute. Add curry paste and cook, stirring, until paste is brick red, about 2 minutes more. Stir in tomato sauce, brown sugar, and cayenne and cook, stirring occasionally, until sauce slightly thickens and becomes dark red, about 10 minutes. Add milk and broth and cook, stirring, until warmed through, 4 to 5 minutes. Stir in fish sauce. Return chicken and any accumulated juices to pan.
Divide rice among plates. Spoon sauce and chicken over. Top with cilantro. Serve with lime wedges alongside.
