Preheat oven to 350° and move rack to lower middle position. Butter and flour bundt pan, or use a baking spray containing flour. If using layer cake pans butter pans, line bottom with parchment paper, butter and flour paper and pan.
Combine lemon zest with 3 tbsp of the lemon juice. Set remaining juice aside for glaze. Set zest and juice mixture aside for 10-15 minutes for zest to soften.
Whisk flour, baking powder, baking soda and salt in a bowl. Set aside.
Whisk lemon zest/juice mixture, buttermilk, lemon oil (if using) and vanilla in a measuring cup. Set aside.
In a small bowl, whisk eggs and yolk to break up and combine them well. Set aside.
In the stand mixer with the paddle beater, cream butter and sugar at medium high speed until light and fluffy, approximately 3 minutes. Scrape down bowl and beater; mix again on medium speed to ensure all the butter is mixed thoroughly.
On medium speed, add half of eggs, mixing until well combined; repeat with remaining eggs and scrape down bowl and beater.
Reduce to low speed and add about ⅓ flour mixture, followed by ½ the buttermilk mixture, mixing each until just combined. Add half of remaining flour mixture, followed by remaining buttermilk mixture, beating until just combined. Scrape down bowl and beater; add remaining flour and mix on low until just combined.
Take bowl off mixer; scrape down bowl and beater and fold batter gently to finish mixing.