Beat the eggs and sugar; add the oil, juice and vanilla alternately with the flour, baking powder and salt. (If you are mixing by hand, combine the dry ingredients first.)
Pour half the batter into a bundt or tube pan sprayed with non-stick cooking spray. You can also use a 9x13 inch pan.
Top with half the apple slices. Combine the 3 tablespoons sugar and 2 teaspoons cinnamon and sprinkle half the mixture over the apples.
Top with remaining batter, apples and cinnamon sugar.
Bake at 350 degrees for 1 hour and 10 minutes.
Cool in pan 1 hour, then remove to serving platter.
To make glaze: melt the butter in a small saucepan over medium/low heat. Stir in the sugar and milk and boil 3 minutes, stirring constantly, until the sugar crystals are dissolved. Cool several minutes, to drizzling consistency, then spoon over the cake, letting some of the glaze drizzle down the sides.