Preheat the oven to 300°F and place a rack in the middle of the oven.

Place garlic halves cut side down in a small baking dish. Drizzle with olive oil, and sprinkle with salt and pepper. Cover the baking dish tightly with foil, then transfer to the oven. Cook until the garlic is tender and golden (about 1 hour). Let the halves cool completely.

Add garlic to a jar with the vodka. Let sit for 24 hours at room temperature, then pour through a fine-mesh basket strainer into a clean container. Cover, and store in the refrigerator for up to 1 - 2 months.