Place 5 ½ cups of flour in the bowl of your stand mixer. Add the salt, sugar, and yeast. Mix with the dough hook on low speed until combined, about 2 minutes. 

In a separate bowl, whisk together the eggs, water, and oil until smooth.

With the mixer running on low, slowly pour the wet ingredients into the dry ingredients. Mix until a sticky dough forms for about 2 minutes.

Continue mixing on low speed, adding more flour about ¼ cup at a time, until the dough pulls away from the sides of the bowl but still sticks slightly to the bottom, about 2 minutes. Avoid adding too much flour – the dough should stay soft and slightly moist.

Increase mixer speed to medium-low and knead for 2-4 minutes, until the dough is smooth and elastic. Then turn the dough out onto a lightly floured surface and knead it by hand for about 1-2 minutes, adding just enough flour to keep it from sticking. The dough should stay soft and slightly tacky.

Lightly oil a large bowl. Place the dough into the bowl, turning it to coat all sides with oil. Cover the bowl with plastic wrap and a tea towel. Let rise in a warm place until almost doubled in size, about 1-2 hours.

After rising, gently punch down the dough to release air. Turn it out onto a lightly floured surface. To make two large challahs, divide the dough in half, then cut each half into 3 or 4 equal pieces and braid as desired. To make three regular-sized challahs, divide the dough into three pieces, then cut each piece into 3 or 4 equal pieces and braid as desired. 

Place the braided dough on a parchment-lined baking sheet. Cover loosely with oiled plastic wrap and let rise for 30-60 minutes, until puffy and almost doubled.

Whisk an egg with a little water and a pinch of salt. 

Preheat the oven to 350F. Gently brush the loaves with the egg wash. Sprinkle with seeds of choice or flaky salt. Bake for 25-30 minutes, checking after 20 minutes. If the tops brown too quickly, reduce oven temperature to 325F and tent the loaves loosely with foil. The bread is done when an instant-read thermometer inserted into the center reads 185–195F.

Transfer loaves to a wire rack to cool completely.

Leftover challah, stored in an airtight container at room temperature, is best eaten within 2-3 days.