In a medium bowl, whisk together the egg yolks and butter. Add the water and whisk until well combined. Set aside.
Using a stand mixer with a paddle attachment, combine the flour, sugar, yeast, and salt. Add the egg yolk mixture and mix for about 1 minute, or until well combined. Switch to the dough hook and knead on medium speed for about 10 minutes. The dough should be soft; add a little more flour if it’s too sticky.
Preheat the oven to 350°F (176°C). Transfer the dough to a clean, oiled bowl. Cover it with a kitchen towel and let it rise in a warm place, or in a 100°F (37°C) warm oven, for about 60–70 minutes, or until spongy.
Turn out the dough onto a flat surface dusted with flour. Knead it by hand and cut it into 6 equal pieces. Cover with a towel and let it rest for about 15 minutes.
Line a baking sheet with parchment paper. Roll each piece of dough into a log about 10 inches (25 cm) long. Fold the log into a knot (refer to the video in my Garlic Parmesan Dinner Roll recipe). Transfer the knots to the baking sheet and brush them with the beaten egg white. Let them rise for about 30 minutes, or until puffy. Repeat the egg wash and sprinkle with salt.
Bake for about 20 minutes, or until the challah knots are golden brown and shiny. Remove from the oven and serve warm.