Preheat oven to 425°F. Line 12 (½-cup) muffin cups with paper liners or coat with cooking spray.
Thoroughly combine goat cheese (or cream cheese), honey, lemon zest and ¼ teaspoon vanilla in a small bowl. Set aside.
Whisk flour, baking powder, baking soda and salt in a large bowl. Lightly beat eggs and egg white in a medium bowl; add brown sugar and the remaining 1 teaspoon vanilla and whisk until the sugar is dissolved, about 1 minute. Gradually whisk in buttermilk and oil until smooth. Add the wet ingredients to the dry ingredients and stir until just combined; do not overmix. Fold in figs.
Spoon half the batter into the prepared muffin cups. Add 1 generous teaspoon of the reserved cheese filling to the center of each muffin, and cover with the remaining batter. (The filling should not be visible.) Sprinkle the muffins with sugar.
Bake the muffins until the edges start to brown and the tops spring back when gently pressed, 13 to 15 minutes. Let cool in the pan for 5 minutes before turning out onto a wire rack to cool.