In a large bowl, whisk together the lukewarm water, whole eggs, egg yolk, oil, honey, and sugar until the honey has dissolved and the mixture is uniform. Set the reserved egg white aside in the refrigerator for the wash.
Add the bread flour and instant yeast. Mix with a dough whisk or the paddle attachment just until no dry flour remains. The dough will look shaggy and rough. That’s what you want.
Cover and let the dough sit for 20 minutes. This is a short autolyse, shortened because the eggs are already in the mix. The flour hydrates and the knead that follows gets a lot easier.
Sprinkle the salt over the dough and knead until it passes the windowpane test and feels satiny rather than tacky. That’s 8 to 10 minutes by hand, or about 6 minutes on a mixer hook at medium-low. Don’t stop early because it still looks loose. Stretch a piece thin and look at the light coming through it.
Peel and dice the apple into 1/4-inch pieces. Toss with the lemon juice so it doesn’t brown while it waits. If you’re using raisins, soak them for 10 minutes in warm water and pat them dry. Wet raisins will bleed into the crumb.
Cover the dough and let it rise at 74 to 76°F (23 to 24°C) for 60 to 75 minutes, until it’s visibly puffy. You’re not looking for a full double here. Puffy and relaxed is enough.
Turn the dough out and gently stretch it into a rough rectangle. Scatter the apple and raisins evenly across the surface. Give it a letter fold, bringing one third over the center and the other third over that.
Twenty minutes later, give the dough a single gentle coil fold to distribute the fruit and rebuild a little tension. That’s it. Stop handling it after this until you’re ready to shape.
Divide the dough into 4 equal pieces. Use the scale. Eyeballing it gives you a lopsided crown, and you’ll see it the second it comes out of the oven.
Roll each piece into a strand 14 to 16 inches long, slightly thicker in the middle and tapered at the ends. If a strand shrinks back, let it rest for 5 minutes, then roll again. Let the dough relax instead of forcing it.
Work on parchment. Lay two strands horizontally and two vertically, weaving them over and under where they cross in the center, like a tic-tac-toe grid. Alternate over and under at each crossing. You will have eight loose ends around the woven center.
Find an end lying under its neighbor and bring it over that neighbor. Work counter-clockwise around the center, making four crossings. Reverse direction and work clockwise for the next round. Keep alternating directions, bringing the lower end over its neighbor each time, until the ends are too short to cross.
Tuck all eight loose ends underneath the woven loaf and pinch them into the base. Gather the loaf into a compact round crown without stretching the strands tight. Every end needs to be secured underneath so it cannot lift and unravel in the oven.
Transfer the shaped crown to a parchment-lined sheet pan. Cover loosely and proof for 45 to 70 minutes, depending on your kitchen temperature. A 76°F (24°C) room lands near 45 minutes. A 68°F (20°C) room needs the full 70 minutes or more.
About 25 minutes into the proof, preheat the oven to 375°F (190°C) with a rack in the center position. Give the oven a full 25 minutes to come completely up to temperature.
Check the proof. Flour a fingertip and press gently into the side of the dough about half an inch. The indent should spring back slowly and leave a faint mark. If it springs back instantly, give it another 15 minutes. If the dent stays put and the dough sighs, get it into the oven.
Just before baking, whisk the reserved egg white with 1 teaspoon of water. Brush the loaf with a full, even coat of egg wash, getting into the crevices between the strands. Sprinkle with sesame seeds now if you’re using them.
Bake for 28 to 35 minutes. The crust should come out deep gold, not mahogany. Check the internal temperature in the thickest part of the woven loaf and pull it at 190 to 195°F (88 to 91°C).
Honey browns fast. If the top hits deep gold before 25 minutes, tent loosely with foil and keep baking to temperature. Color is not doneness.
The moment it comes out of the oven, brush the hot loaf with warmed honey. It sets into a light shellac as the loaf cools, and it’s the difference between a good challah and one people remember.
Cool on a rack for at least 45 minutes. Cutting a hot enriched loaf collapses the crumb and compresses the braid. I know it’s hard. Wait anyway.