In a small heavy skillet, heat sugar until golden brown. Gradually add water; cook & stir until sugar is dissolved. Set aside.
Let egg whites stand at room temperature for 30 minutes. In a large bowl, combine the flour, sugar, baking powder & salt. In another bowl, whisk the egg yolks, oil, water, vanilla & 6 Tbsp reserved syrup. Add to dry ingredients; beat until well blended. In another bowl, beat egg whites & cream of tartar until stiff peaks form; fold into batter.
Gently spoon into an ungreased 10" tube pan. Cut through batter with a knife to remove air pockets. Bake on the lowest oven rack at 325 degrees F. for 45 - 50 minutes or until cake springs back when lightly touched. Immediately invert pan; cool completely, about 1 hour.
Run a knife around side & center tube of pan. Remove cake to a serving plate.
For frosting, in a small saucepan, melt 2 Tbsp butter. Stir in flour & salt until smooth; gradually add remaining syrup mixture. Bring to a boil; cook & stir for 1 minute or until thickened. Transfer to a small bowl; beat in the confectioners’ sugar, milk & vanilla. Cool to room temperature.
In a large bowl, beat remaining butter until fluffy, about 5 minutes. Gradually beat in confectioners' sugar mixture. Spread frosting over top & sides of cake.
TO MAKE AHEAD:
Cake can be made the day before serving. Store the cake tightly wrapped at room temperature. The remaining caramelized sugar for the frosting can also be stored covered at room temperature overnight.