In the bowl of your stand mixer, whisk together the flour, salt, cream of tartar, baking soda, sugar, and instant yeast. Fit the mixer with the paddle attachment and add the vinegar, eggs, lactose-free milk and melted butter, and mix to combine. Mix on low speed until the liquid is absorbed by the dry ingredients, then turn the mixer speed to high and mix for about 3 minutes or until everything is very well combined. The dough will be slightly wet.
Place the donut dough .in a lightly greased bowl or container, cover it and place it in a warm spot to rise for about 1 hour or until double in size. (you can keep the dough for up to 2 days in the refrigerator).
When you’re ready to work with the dough, turn it out onto a lightly floured surface. Line rimmed baking sheets with unbleached parchment paper and set them aside. Sprinkle the dough lightly with some extra flour. Using a rolling pin, lightly roll it out to about 1inch (2.5cm) tick.
Using a round cookie cutter or a jar, cut the doughnuts rounds and place them on the prepared baking sheet, leaving space apart. Cover the baking sheets with oiled plastic wrap, and place in a warm spot. Let them rise for about 40min.