Brush this on chicken, pork, or steak when the meat is almost finished grilling; the sauce should caramelize but not burn. Serve more sauce at the table.
Soak figs in 2 cups boiling water until soft, about 5 minutes; drain. Pulse with vinegar, tomato paste, and 1 teaspoon salt in a food processor, scraping down sides often, until pureed, about 3 1/2 minutes. Heat oil in a saucepan over medium heat. Cook garlic for 30 seconds. Pour in fig puree. Whisk in 1 cup room-temperature water and bay leaf. Reduce heat to low. Simmer for 15 minutes. Season with 1/2 teaspoon salt. Discard bay leaf. Refrigerate until ready to use (up to 2 months).