Combine balsamic vinegar and figs in a small saucepan over high heat, and bring to a boil. Reduce heat, and simmer until reduced to 1/3 cup (about 5 minutes). Combine the fig mixture, 6 tablespoons water, and lemon juice in a blender, and process until smooth.
Place the fig mixture in a small bowl. Stir in shallots, thyme, and garlic. Add extravirgin olive oil and salt; stir well with a whisk.