Add salt + oil, stir again. Now add half of the flour + egg + egg yolk + cardamom and start kneading with a dough hook attachment. Add little flour as needed. The dough should be sticky and elastic. The dough should be soft and when you touch with your fingers it should not be sticky. Reserve about 1/2 cup of flour.
Transfer the dough onto a lightly floured work surface and knead well with the palm of your hands for 6-8 minutes so that the gluten can develop. Add the reserved 1/2 cup of flour as needed. (If you have a stand mixer you can knead in it all the way through and you dont have to knead by hand)
Punch down the dough, separate it into 2 equal parts. Further divide each part into 6 parts. Roll 6 ropes about 15 inches long. Keep it parallel to each other. If its difficult to roll, cover and try doing it after 5 minutes.
Take the right strand, bring it below the middle strand, then move it to the left.
This song will help you (Over the two - under the one - over the two). Repeat the same till you reach the end of the strands.
Pich the other side together.
Tuck both the sides under the dough and slowly plump it up with the palm of your hands.
Carefully transfer this to a non-stick mat or parchment paper lined baking sheet.
Cover with a lightweight damp Kitchen towel. Let it rest for additional 30 to 45 minutes.
Gently brush the top of challah with egg wash. Apply generously in the corners and towards the sides too.
Bake for 25 to 30 minutes until you achieve a brown shiny look.
If you don't want the challah to be sweet, use only 1/4 cup of honey. You can also choose not to use cardamom.