Prepare chicken. Combine Calabrian chilies, honey, olive oil, red wine vinegar, garlic, tomato paste, smoked paprika, salt, pepper, coriander, and anchovy paste in a medium bowl. Whisk until well combined. Set aside ¼ cup marinade.
Pour remaining marinade over chicken, turning to coat. Let sit for 1 hour or up to overnight.
Meanwhile, prepare lemon herb oil. Combine parsley, basil, olive oil, and the juice of ½ lemon in a medium bowl. Season with salt and pepper and set aside.
Preheat oven to 400 degrees F. Line a baking sheet with parchment paper.
Cut the top off the garlic head to expose garlic cloves. Drizzle with olive oil and season with salt and pepper. Wrap garlic in aluminum foil and place on prepared baking sheet. Arrange chicken on baking sheet. Roast for 20 minutes. Remove chicken and baste with reserved marinade. Roast for another 20-25 minutes or until the internal temperature of the chicken registers 165 degrees F.
Unwrap garlic and squeeze to remove garlic cloves. Transfer cloves to a medium bowl and mash with a fork until smooth. Add yogurt and lemon juice and season with salt and pepper.
Spoon roasted garlic yogurt sauce on a serving platter and arrange chicken on top. Drizzle lemon herb oil on top or serve on the side.
Notes
You can prepare the roasted garlic yogurt sauce and lemon herb oil the day before.