Make the sponge: In your stand mixer bowl (or a large bowl, if doing by hand), whisk one cup (128g) of the flour with the yeast, and stir in the lukewarm water until the sponge is smooth. Cover with plastic wrap or a dish towel and let it rise for about 45 minutes, until puffy and bubbly.  

Make the dough:  Directly into the bowl, add the salt, honey, oil and eggs. Stir until well mixed, then add the remaining three cups (384 g) of flour (note, this only takes you to the 4 cups, not 5).

Stir until the dough forms a sticky mass. If you have to, add a bit more flour, but keep it as minimal as possible to ensure a fluffy bread at the end.  If using a mixer, knead on medium-low for a minute or two, or knead manually on a lightly-floured surface.  You want the dough to become smooth.

Then transfer to a lightly oiled bowl, cover it with dish towel or seal with plastic wrap (my preference), and let it rise in a warm spot until doubled in bulk.  This will take 1-2 hours, or possibly longer depending on the temperature of your kitchen. (Note: you can make the dough to this point, punch it down, and stash it in the refrigerator overnight).

Shape the dough:  Punch down and divide the dough into three or four parts, depending on what shape you want to make.  Roll each portion into a ball. Let them rest for 10-15 minutes (I put the plastic wrap over them to prevent a skin forming).

Roll each ball into long ropes (at least 12 inches in length for the 4-braided challah) and braid into desired shape.  I have detailed pics and instructions for shaping into the 4-strand round in the post above, and link to the video instructions I followed.

Transfer to a greased or parchment-lined baking sheet and brush with the first egg wash (the egg + water one).  Let the loaf rise for about 30 minutes (I put a giant plastic bag over it to protect it a bit, but the egg wash will probably do this too.  

Preheat the oven to 350 F.  Place another baking sheet underneath your first baking sheet (this helps insulate the bottom and keep it from burning).

Right before putting in the oven, brush your second egg wash on (the egg yolk + sugar one) and sprinkle with the flaky sea salt.  You can sprinkle with poppy seeds if you like as well.

Bake for 45 to 50 minutes, checking after 40 minutes. Cool completely before slicing (the inside should be at least below 80 F before cutting into it).