Whisk the soy sauce, lime juice, oil, garlic, cumin, paprika, oregano, pepper, and salt. Rub over and under the chicken skin. Cover and refrigerate for at least 12 hours.
Set the chicken skin-side up on a wire rack over a baking sheet and let it stand at room temperature for 30 minutes while the oven heats to 425 F (220 C).
Roast:
Roast the chicken for 50 to 65 minutes, rotating the pan once, until the breast reaches 165 F (74 C) and the thigh reaches at least 175 F (80 C).
Rest the chicken for 15 minutes before cutting into serving pieces.
Sauce and Fries:
Blend the coriander, jalapeno, mayonnaise, queso fresco, and lime juice until mostly smooth; chill until serving.
Toss the potatoes with oil and salt. Roast on a second tray for 35 to 45 minutes, turning once, until browned. Serve with the chicken and sauce.
Notes
For darker edges, broil the rested chicken for 2 to 3 minutes while watching closely.