Add 1 egg, 2 yolks, the lukewarm water, and 2 tablespoons of vegetable oil to a stand mixer with a whisk attachment and mix until combined.
Switch to the dough hook. Add in the flour and instant yeast. Run on low for 3-4 minutes. Rest for 20 minutes while the flour hydrates.
Add in 1/4 cup granulated sugar and 1 teaspoon of salt. Run on medium speed for 9 minutes.
Quickly hand knead to make sure it doesn't stick to the counter. If it does, add a little more flour. Lightly oil the bowl and the dough, cover, and rise for 1.5 hours until just about doubles in size. If your bowl has a lid, you can seal it. If not, cover the bowl with a kitchen towel, and seal the bowl (and kitchen towel) in a garbage bag to trap in the air.
Punch down the dough, divide, and braid. Divide the dough into 4 equal 16-inch long ropes with the ends tapered. See photos for braiding instructions.
Stack two baking sheets** and top with a layer of parchment or a silicone baking mat. Cover with cling wrap and prove for 3 hours. It will double in size.
Heat oven to 350F with the rack in the middle.
Mix the remaining egg with the (optional) honey* in a bowl. Brush over the challah. Sprinkle with the sesame/poppy seeds.
Bake 35-40 minutes until the internal temperature reads 190F.
LET IT REST! 30 minutes minimum. This is the hardest part but it is well worth it.
Video
Notes
LET IT REST after baking! 30 minutes minimum. This is the hardest part but it is well worth it.If you happen to have leftovers...make some French toast!Bake until internal temperature reads 190F. This is a better indicator of the bread being done than time.Cook the challah in a springform pan if you're planning on making french toast the next day... it yields a better shape for slicing!*If you use the honey in the glaze, it will get brown much faster. So cover it with tin foil once it starts to get golden to prevent burning.** Stacking two baking sheets helps keep the bottom from browning/burning.