Pour warm water into a large mixing bowl. Drizzle the yeast and sugar over the warm water and stir just until incorporated. Let it sit to proof for 15 minutes, or until you see a layer of foam on top of the water.
While the yeast is sitting, crack 1 egg into a small bowl. Add the oil to the egg and whisk to incorporate.
When the yeast mixture is foamy/bubbly/active, pour in half of the flour and all of the salt into the bowl with the active yeast. Mix well.
Add the egg mixture to the large bowl and mix.
Slowly add the rest of the flour in 1/4 cup increments. (Leave some flour to add during kneading. It is not necessary to finish all of the flour. You may have some left which you can use to help with the braiding process.) Mix until thoroughly combined, then knead for 5-10 minutes until there is a smooth texture and it doesn't stick to the bowl.
Grease the top of the bowl with a little oil and cover with plastic wrap and/or a clean towel. Set aside and rise for 1 hour in a warm, draft-free spot.
While the dough is rising, preheat oven to 360° F.
Line a large baking tray with parchment, or use 2 parchment-lined baking trays if one is not large enough for both loaves. Braid the challahs then place them diagonally on the parchment-lined baking tray(s). If putting both loaves on one tray, leave enough space between them to rise.