Preheat the oven to 375 degrees F.
Toast the coriander seeds, mustard seeds, peppercorns, cumin and bay leaf in a dry pan until fragrant and the mustard seeds begin to pop, about 1 minute. Transfer to a spice grinder or small food processor and grind into a fine powder.
Place the chicken in a roasting pan and pat dry. Arrange the carrots and onions around the chicken. Scatter the orange zest on top of the chicken and place the orange pieces in the cavity.
Lift the chicken skin from the chicken without removing it using your fingers. Rub the spice mixture and the salt on top of the chicken and under the skin. Pour the beer into the bottom of the roasting pan, not onto the chicken or any of the vegetables. Cover with foil and carefully transfer to the oven.
Roast the chicken for 30 minutes, and then remove the foil and return to the oven and continue cooking until the internal temperature reaches 160 degrees F, 30 to 40 more minutes.
Let rest for at least 10 minutes before cutting into halves or quarters. Remove the orange and skin before serving.
Nutrition information per serving: 411 calories, 11 g fat