Preheat oven to 425°. Coat a wire rack with nonstick spray and set inside a baking sheet.
For the chicken, cut breast pieces in half; season pieces with pepper. Combine almonds, panko, and sage in a dish. Place buttermilk in a separate dish.
Dip chicken pieces in buttermilk, roll in almond mixture to coat, and place on prepared rack.
Roast chicken until crisp and golden brown, about 50 minutes. Chicken is cooked when an instant-read thermometer inserted into the thickest part registers 165° for white meat and 175° for dark meat. Remove from oven.
For the gravy, heat broth and milk in a saucepan over medium-low until simmering.
Melt butter in a medium saucepan over medium heat. Whisk in flour; cook until roux is a light tan color, about 2 minutes. Whisk in broth mixture until there are no lumps.
Stir in thyme, salt, vinegar, and pepper, and cook until the gravy thickens, 3–4 minutes.