In a mixing bowl, beat 1 cup of sugar, vegetable oil, one egg and milk with an electric mixer. Beat in lemon zest and juice. Set bowl aside.
In a second mixing bowl, whisk together with a fork your flour and baking soda.
Pour lemon mixture slowly into flour mixture and blend together until just moistened with a spoon (not your mixer).
Pour batter into prepared muffin tins but only about halfway full. Set aside.
In another mixing bowl, beat cream cheese, remaining 1/2 cup of sugar, remaining egg, and vanilla extract with an electric mixer. Slowing top off each of your muffins with a little cream cheese mixture (you will not use all of your cream cheese mixture).
Pop your muffin tins in the oven and bake about 12 minutes for mini-muffins and 18 to 20 minutes for larger muffins.
Remove from oven and allow to cool before removing from pan.