In a mixing bowl, whisk together flour, baking powder, and salt. Set aside.
In a second mixing bowl, beat together the butter and sugar until fluffy and lightened in color. Add the eggs one at a time, beating well after each addition. Scrape the sides and bottom of the bowl once all the eggs have been added, and beat briefly to re-combine any residue.
Add ⅓ of the flour mixture to the batter and mix on low speed to combine. Add ½ of the milk and mix to combine. Mix in another ⅓ of the flour. Mix in the remaining milk. Mix in the remaining ⅓ flour. Stir in the grated lemon rind or lemon oil.