In a small bowl pour boiling water over figs to cover; let stand 15 minutes. Drain well.
Meanwhile, in a medium bowl stir together chevre, sour cream, basil, milk, and thyme. Season to taste with salt and pepper. Stir in drained figs and half the walnuts. Cover and chill in refrigerator up to 24 hours.
To serve, transfer spread to serving bowl. Sprinkle with remaining walnuts and fresh thyme sprigs. Serve with baguette slices or crackers. Makes about 1-1/2 cups (twelve 2-tablespoon servings)