MAKE THE DOUGH. Dissolve the salt in the melted butter and set aside to cool.
In the bowl of a stand mixer, whisk the water, yeast and sugar to combine; let sit for 5 minutes.
Add the butter to the yeast mixture and whisk to combine.
Add the flour and mix, using the dough hook, until a slightly tacky dough forms; it should not stick to your fingers. If it is too tacky, add up to an additional ¼ cup of flour.
Lightly flour a clean work surface and knead the dough until smooth, about 5 minutes.
Shape the dough into a ball and transfer it to a bowl that has been coated with non-stick spray.
Cover the bowl with plastic wrap and allow the dough to rise until doubled in size, about 1 hour.
Punch down the dough, flip and let proof for an additional 30 minutes.
Meanwhile, in a large stockpot, bring 8 cups of water to a boil.
Add the baking soda and stir to combine.
When the dough has risen, cut it into quarters.
Roll each quarter segment into a rope; place plastic wrap or a clean tea towel over any dough not in use to keep it from drying out.
Using a knife or bench scraper, cut the dough into ½-ounce pieces, about the size of a half dollar.
Roll the pieces into balls.
Cook the dough balls, in batches, in the boiling water for 30 seconds.
Using a slotted spoon, transfer the cooked dough balls onto a sheet pan lined with a silicon baking mat or parchment paper.
Preheat the oven to 450-degrees.
Meanwhile, MAKE THE EGG WASH. In a medium bowl, vigorously whisk the egg and salt to combine.
Using a pastry brush, lightly brush the dough balls with the egg wash.
Sprinkle each ball generously with fleur de sel.
Bake the pretzel bites until deep golden brown, for 15-20 minutes.
Cool at least 15 minutes before serving.