1vanilla beansplit lengthwise and seeds scraped out (or 1 tsp pure vanilla extract)
1tbspfinely grated lemon zestoptional
1/4cuplemon juiceor water, for plain vanilla cake - see above
2tbspmilkor lemon juice
1/8tspvanilla extractomit if using lemon juice
Preheat oven to 350º. Line an 9x5" loaf pan with parchment paper.
In a large bowl, whisk together flour, baking powder and salt. Set aside.
Combine butter and sugar in standing mixer and beat on medium speed until very light and fluffy, about 4 minutes. Beat in eggs one at a time, beating for about 15 seconds after each and pausing to scrape down sides of bowl before adding the next. Beat in vanilla bean seeds.
With mixer speed on low, gradually beat in half of the flour mixture. Stop mixer, scrape down sides of bowl, then beat in milk on low speed, followed by remaining flour mixture. Scrape batter into prepared pan and bake 45 minutes - 1 hour, until tester inserted in centre comes out clean. Place on wire rack for 10 minutes to cool in pan, then carefully invert cake directly onto rack. Peel off parchment paper and invert again so that it's right-side up.
To make glaze:
Combine sugar and lemon juice in a small saucepan over medium heat until sugar is dissolved. While cake is still warm, poke several holes in the top with a toothpick and brush glaze over repeatedly until it's all used.
To make frosting:
Beat all ingredients together on medium speed of electric mixer until light and fluffy. Spread on completely cooled cake.