Preheat oven to 350° F or preheat doughnut maker. In a large bowl, whisk together flour, sugar, baking powder, salt, and lemon zest if using, until well combined. In a one cup measuring cup, add vinegar and milk and let sit for 5 minutes.
In a separate, smaller bowl, beat egg until white and yolk are somewhat combined, then pour in milk/vinegar mixture followed by the melted and cooled butter and vanilla. Pour wet ingredient mixture over dry ingredient mixture, and whisk/stir until thick. smooth batter forms. Do not over-mix.
Pour mixture into a piping bag or ziploc plastic bag and snip off a 1/2 inch hole. Pipe donut batter either into greased donut pan or into preheat donut maker coated with cooking spray, filling cavities halfway.
Bake in oven for 5 to 7 minutes or in donut make for 4 minutes, or until toothpick inserted in center comes out clean. Remove donuts and let cool while you prepare a station for powdering.
Add powdered sugar to a brown paper bag or ziploc plastic bag, making sure there is enough empty space for donuts to move around. Add melted butter to a small bowl. Working two at a time, dip donuts in melted butter, then drop into bag filled with powdered sugar. Close bag and shake gently to coat in sugar. Remove and set on a plate to dry.
If needed, return donuts to bag and shake again until enough powdered sugar has coated the donuts. Do not dip in melted butter again, just shake in bag. (the butter will melt the powdered sugar!)