Mix the half cup of lukewarm water with yeast and 1 tbsp of the honey and set aside for 5 minutes. The water should be warm to the touch but not hot.
Combine flour, salt, egg, oil, and remaining honey in a medium mixing bowl. Add water, honey, and yeast mixture. Gently mix together ingredients by hand until a soft, sticky dough forms.
Turn out dough onto a lightly floured surface. Knead the dough until smooth and passes the window pane test. Lightly grease the bowl with oil and place the dough back in.
Cover the bowl with plastic wrap and set aside. Let the dough rise for about 2 hours until roughly doubled in bulk.
Gently deflate the dough and turn out onto a lightly floured surface. Divide into 3 or 6 even pieces depending on your preferred style of braid. Roll each piece into 15'' to 20'' long strands.
Mix together your honey and crushed walnuts. Generously cover one side of each dough strand with the mixture, using a spatula or clean hands.
Braid the loaf. See videos linked above for the technique. Make sure to turn the honey-covered side inwards so the outside of the loaf is smooth. A little bit of honey and walnut leaking out is okay.
Gently place the braided loaf on a parchment paper or aluminum foil-lined baking sheet.
Cover the loaf with lightly greased plastic wrap and let rise for 90 minutes to 2 hours until puffy. When you poke with a finger, the indent should slowly fill back in about halfway. Towards the end of the rise, preheat the oven to 375 degrees Fahrenheit.
Make the egg wash by whisking together the egg and water or milk. Brush the top of the loaf with the egg wash. You can use either a pastry brush or clean hands.
Insulate the bottom of the loaf by stacking your baking sheet on another baking sheet, or double-lining with parchment paper. Place the loaf in the bottom 1/3 of the oven and bake for 20 minutes. If it's a deep golden brown, tent with aluminum foil. Otherwise bake for another 5-10 minutes until desired color is achieved.
After tenting with foil, bake for another 10-15 minutes.Remove from the oven and place on a wire cooling rack.