Tangy sweet lemon glaze tops a nice dense and not too sweet vanilla cake muffin. Use the servings slider if you'd like to change the number of servings.
Preheat the oven to 425°F. Lightly grease a 12-cup muffin tin, or line the tins with 12 muffin cups, and spray the cups with non-stick vegetable spray.
In a medium bowl, mix the butter, oil, and sugars together until smooth. Add the eggs, beating to combine.
Stir in the baking powder, baking soda, salt, and vanilla. Alternating, stir the flour and milk into the butter mixture, beginning and ending with the flour, and thoroughly combining the ingredients.
Spoon the batter evenly into the prepared muffin tins, filling the cups nearly full. Bake the muffins for 15 to 17 minutes, or until they're pale golden brown and a cake tester inserted into the middle of one of the center muffins comes out clean.
Remove the muffins from the oven, and let cool for a couple of minutes, or until you can handle them.
While they're cooling, make the lemon glaze.
Lemon Glaze:
In a small bowl, combine the lemon juice and powdered sugar, stirring well with a whisk. Drizzle or spoon the glaze on top of the muffins. Depending on how much glaze you like, you may have extra glaze leftover.
Serve warm, or cool on a rack and wrap airtight. Store for a day or so at room temperature.