Preheat oven to 425°. Season chicken with 1 tablespoon salt, pepper, and poultry seasoning; let stand at room temperature for 40 minutes. Pat dry.
Heat a 12-inch enamel-coated cast-iron skillet over medium heat; add oil, swirling to coat. Add chicken, skin side down; cook, without turning, until skin is browned and crisp, about 15 minutes. Transfer chicken to a large plate.
To skillet, add grapefruit slices, onion wedges, thyme, and rosemary. Smash 3 garlic cloves and scatter around skillet; stir to coat grapefruit mixture in drippings. Arrange chicken on top, skin side up.
Bake until an instant-read thermometer inserted in the thickest part registers 165°, about 15 to 18 minutes. Remove from oven, and discard rosemary and thyme sprigs. Let chicken stand for about 5 minutes.
Meanwhile, grate remaining 1 clove garlic into a medium bowl. Stir in chopped grapefruit, chopped onion, jalapeño, vinegar, honey, and remaining ¼ teaspoon salt. Serve over chicken quarters. Garnish with thyme, if desired.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/roasted-chicken-grapefruit-relish/