Marinate the chicken: Put the chicken in a large zip-top bag with the beer and vinegar. Seal and refrigerate at least 6 hours or overnight.
Make the spice rub: Pulse the garlic, oregano, olive oil, serrano chile, cumin seeds, paprika, 2 teaspoons salt and 1 teaspoon pepper in a mini food processor to make a paste. (If you don't have a mini food processor, finely chop the garlic, oregano and chile, then whisk in the spices and olive oil.)
Remove the chicken from the marinade and pat dry with paper towels. Rub all over and under the skin with the spice rub, put on a rack set on a rimmed baking sheet and let sit at room temperature 30 minutes. Preheat the oven to 350 degrees F.
Brush the chicken lightly with olive oil and roast until slightly golden, 30 minutes. Increase the oven temperature to 450 degrees F and continue roasting until the chicken skin is golden brown and crisp and a thermometer inserted into the thickest part of the breast registers 165 degrees F, about 25 more minutes. Remove the chicken from the oven, brush the skin with the pan drippings and let rest 10 minutes. Transfer to a platter and season with salt.