If possible, grind fresh cardamom by toasting the pods lightly in a dry pan; remove the shell and grind the seeds using a mortar and pestle. Set aside until the ground cardamom is ready to use.
If using active dry yeast, heat the milk in the microwave or on the stovetop until it is “fingervarm” (finger warm), meaning it should feel warm to the touch but not hot. Add your yeast, a small amount of the sugar needed for the recipe, stir, and leave it for 5-10 minutes until the mixture starts to bubble up. You can add this to the bowl of a stand mixer or another mixing bowl. If using instant yeast, simply add the yeast to the lukewarm milk – there usually is no need to wait for it to bubble up, but follow the instructions on your package of yeast if in doubt!
Combine eggs, the remaining sugar, cardamom, vanilla extract, and salt in the bowl with the yeast and the milk mixture.
Add in the flour and mix until the dough begins to come together.
Add in softened butter and continue to knead the dough for at least 10 minutes until smooth and elastic.
Cover the dough and let it proof in a warm place for 1.5-2 hours, or until doubled in size.
Once the dough has proofed, prepare the filling mixture: combine light or dark brown sugar in a bowl with ground cardamom; melt butter and keep in a separate bowl.
Cut the dough into quarters, then roll each quarter into a log; proceed to cut the log into small pieces, about 20-25 pieces per quarter. You'll have about 80-100 pieces of dough total.
Grease a 10-inch bundt pan with some of the melted butter (the pan should have a 12 cup capacity; if you use a smaller pan, you will have to bake some of the dough separately so the pan doesn't get overfilled!)
Dip each piece of the dough in the melted butter, then coat in the brown sugar and cardamom mixture. Place each piece in the bundt pan.
Repeat until your bundt pan is about 2/3 of the way full - if you fill this up more, it may leak out onto the bottom of the oven, so if you have leftover dough, you can bake it separately (either in ramekins or a muffin tin would be a good option!)
If you end up with leftover sugar and butter, pour the rest over the top of the dough in the bundt pan.
Cover the pan and let it rest for an additional 30 minutes.
While the dough is rising again, preheat the oven to 350℉ (175℃).
Place the bundt pan in the oven on a lower oven rack so that the top doesn't get too brown. Bake for around 40 minutes - the top will be nice and golden, and the interior temperature of the dough should read 190℉ (88℃). If the top is browning too quickly, you can cover it with foil. If you're worried about leaking, put a baking sheet underneath the pan to catch anything that drips down so it doesn't burn to the bottom of the oven.
Once done baking, let cool for 10-15 minutes. Flip out onto a serving plate or cutting board, and it's best enjoyed while still warm! You can, of course, save the leftovers and reheat them in the microwave.