Preheat the oven to 350 degrees. Grease a deep 12-cup muffin pan.
Melt the butter and let it cool. In a large bowl, beat the cream cheese and sugar together with a hand mixer, on a medium speed. Then add one egg at a time until well combined, and then stir in the melted butter.
Mix the flour and chopped figs in a bowl. Then stir gently into the batter.
Spoon into the muffin pan filling each pan about two-thirds full. Bake for about 20 minutes or until the tops become golden brown. Set the muffins aside to cool on a rack before drizzling the glaze on them.