In large bowl or stand mixer, stir together the yeast, 1 tablespoon sugar, and ¼ cup warm milk. Let sit for 5 minutes (the yeast should be foamy).
In the meantime, mix together the remaining ⅓ cup sugar, ½ cup warm milk, melted butter, and salt. Add that mixture to the yeast once it has proofed along with the egg, Meyer lemon zest, and cardamom. Stir until thoroughly combined.
Add the flour. If using a stand mixer, attach the dough hook and incorporate on low speed. If not, just use a sturdy wooden spoon or rubber spatula. Mix until the dough begins to pull away from the sides of the bowl, about 2 minutes. If the dough is very sticky, add 1 tablespoon of flour at a time until it comes together. Do NOT add more than ½ cup of extra flour, and do your best to add as little as possible, otherwise it will make the doughnuts dry and tough.
Turn the mixer to medium and knead the dough for 5 minutes. Alternatively, you can turn the dough out onto a lightly floured work surface and knead until smooth and elastic, about 8 minutes.
Place the dough into a lightly oiled (clean) bowl, cover, and let rise in a warm, draft free place until doubled in size (1-2 hours depending).
When the dough has doubled, turn it out on to a lightly floured work surface and use a rolling pin to roll it out to about ½ inch thick. Use a doughnut cutter to cut out as many as you can, then reroll the scraps.
Place doughnuts on to two (or more) parchment lined baking sheets, then cover and let rise again until doubled in size.
Preheat the oven to 400 degrees. Brush the tops of the doughnuts with melted butter, then bake for 7 minutes exactly. Do not over bake even if they are not golden brown.
Allow the doughnuts to cool completely. In the meantime, make the glaze. Combine the Meyer lemon zest, juice, milk, cardamom, salt and melted butter in a bowl. Add the powdered sugar and whisk until smooth.
Dip the doughnuts into the glaze to coat on all sides except the very bottom. Transfer to a rack and allow to set up for about 20 minutes before serving.
Optional Step: Place glazed doughnuts back on the sheet pan and pop into a 400 degree oven for about 2 minutes. Remove and let cool before serving.