Put ¼ cup warm water in the bowl of a stand mixer or a large bowl if making it by hand.
Add 1 teaspoon active dry yeast and mix with a spoon. It will be lumpy and weird. Cover with a clean kitchen towel and let stand 3-5 minutes until frothy.
Add 1 cup whole milk, warm, ½ cup sugar, 1 teaspoon vanilla extract, 1 teaspoon ground cardamom, and 2 eggs. Mix a few times until the eggs are combined.
Add 1 and ½ cups flour and 1 teaspoon salt. Mix with the spoon. It will be lumpy and rough.
With the stand mixer: attach the dough hook. At low/medium speed add ½ cup butter, melted, and 3 cups flour, half cup at a time. Stop the mixer, cover the bowl with a clean kitchen towel and let rest for 15 minutes.
By hand: add ½ cup melted butter and 1 and ½ cups flour and mix well with a spoon. Add 1 and ½ cups flour and mix. It will be dry and lumpy.
Cover the bowl with a clean kitchen towel and let rest for 15 minutes.
If using the stand mixer: use the dough hook at medium speed for 6 to 8 minutes, until you have a shiny, satiny but slightly sticky dough. You might use the extra ½ cup flour but don’t be tempted to add more unless the dough is very wet and sticky.
If kneading by hand, do it on a clean surface, ideally marble counter or similar.
Knead while adding the rest of the flour by tablespoons until the dough is shiny, slightly sticky but it’s easy to separate it from the counter. It takes a few minutes to start coming together. You should knead for 8-10 minutes.
Put the dough in an oiled or buttered large bowl (the dough should be able to double comfortably) and turn it onto itself so the whole surface is greased.
Cover with plastic wrap and let rise in a draft-free warm place until doubled, 45 minutes to 1 hour, depending on the temperature of the place. Alternatively, you can refrigerate it for 8 hours. Once you're ready to shape it, take it out of the fridge and wait 15 minutes or so, it depends on how warm your space is. Don't wait too long since the cold dough is much easier to shape.
Have ready a buttered or parchment-lined baking sheet.
When ready to braid, gently punch the dough down and turn it onto the counter or similar surface. Cut the dough into 3 parts and make them into ropes.
Put three ends together, pinch them down and braid them. Then join the ends to make a wrath. Or make 2 braided logs, not a wreath.
Transfer the braid to the pan. Cover with a clean kitchen towel and let rise for about 30 minutes, until slightly puffed.
Preheat the oven to 350ºF (180°).