Combine warm water (at least 110 degrees Fahrenheit up to 120), with 2 teaspoons of sugar and the yeast. Cover with a kitchen towel for 5 minutes until foamy.
Add the salt, honey, oil, eggs, sugar, cardamom and 2 cups of the flour. Using the paddle attachment on your stand mixer, beat the mixture on low for 1-2 minutes, scraping down the sides if needed. Add the remaining 2 1/2 cups flour and continue to beat for a few more minutes.
The dough will look sticky (and it is) so cover your workspace generously with flour, coat your (very dry) hands with flour and start kneading the dough for 7-10 minutes, adding flour as you need it. You may need to add up to 1/4 cup more flour. When done, your dough should be smooth and quite tacky, but should no longer stick to your hands.
Put the dough in a clean, oiled bowl, cover with a kitchen towel and set aside in a warm environment for 1 1/2 hours (90 minutes). If your house is particularly cold, you may want to put it in the oven around 70 degrees Fahrenheit.
Once the first proof is done, remove the dough from the bowl and cut it into 8 equal parts. More detailed instructions with photos on how to form the challah buns are in the post above, but here is the gist. Take one eighth of the dough and cut it in half. Roll each piece into a rope around 12 inches long. Attach the dough at the top, twist the strands together, then roll it up like a snail. Set on a baking sheet with parchment paper. Once you've formed all buns, cover with a kitchen towel and proof an additional 35 minutes. While this is proofing, you can preheat your oven to 375 degrees Fahrenheit.
Finally, mix together your final egg and one teaspoon of water. Whisk well until no white is left. Then brush your buns with the egg wash using a pastry brush, or your fingers if you don't have one. Bake your challah buns (uncovered) for 20-25 minutes until golden brown.