Heat oven to 450 degrees. In a small bowl, mix together cumin, coriander, paprika, oregano and salt. Coat the chicken thoroughly with the spice mixture.
In a large cast-iron skillet, combine potatoes and carrots. Add oil, season with salt and toss to coat. Place chicken on top, skin side up. Roast until chicken is cooked through and skin is crisp, 45 minutes to 1 hour. (An instant-read thermometer inserted into the breast or thigh should read 165 degrees.)
During the last 5 minutes of roasting, in a small skillet, melt butter over medium-low heat. Add garlic and cook, stirring occasionally, until softened, about 3 minutes. Turn off heat and stir in serranos and cilantro. Zest the lime into the pan, then halve the lime and squeeze the juice into the sauce. Season with salt to taste.
Drizzle the butter sauce over the chicken and serve.
