Whisk goat cheese and milk until smooth; add to egg mixture, whisking until smooth. Pour into 4 lightly greased 6-ounce custard cups, and place cups in a 9-inch square pan. Add hot water to pan to depth of 1 inch.
Bake at 375° for 10 minutes; reduce heat to 325°, and bake 35 minutes or until almost set. Transfer to a wire rack to cool. Cover and chill 8 hours.
Process strawberries, liqueur, and 2 tablespoons sugar in a blender or food processor until smooth. Pour through a wire-mesh strainer into a bowl, pressing with the back of a spoon; discard seeds. Chill. Spoon 1/4 cup strawberry sauce on each serving plate; unmold custards onto plates.