Preheat oven to 450 degrees F (230 degrees C).

Slice the top off the half head of garlic with a sharp knife, exposing the cloves. Discard the top. Place the head of garlic on a piece of aluminum foil, drizzle with 1/4 teaspoon of olive oil, and wrap the foil around the garlic. Roast in the preheated oven until golden brown, 30 to 40 minutes.

While garlic is roasting, place the onion and 1 tablespoon of olive oil into a saucepan over medium heat and cook and stir until the onion is browned, 10 to 15 minutes. Remove from heat. Stir in the apricot preserves, vinegar, ginger, cayenne pepper, and salt until thoroughly combined.

Squeeze the roasted garlic cloves out of their skins, and mash them in a bowl with a spoon. Mix the garlic into the chutney; bring to a boil over medium heat. Reduce heat and simmer until thickened, about 25 minutes, stirring occasionally. Stir carefully because any splashes of chutney will be burning hot.

Pack the chutney into sterilized jars and process to seal.