Whisk flour, yeast, salt and brown sugar together in a bowl. Stir in the water with a stiff spatula until the dough just comes together and there are no dry ingredients.
Transfer the dough onto a lightly floured area and knead until the dough holds its shape. This should take about 8 minutes. Form the dough into a ball and place in a lightly oiled bowl. Oil the top of the dough with a tablespoon of oil to prevent cracking. Cover with a warm moist towel and let rise until it doubles in size. This should take about an hour.
Line two baking sheets with parchment paper. Transfer the dough to a lightly floured surface and divide it into eight pieces. Roll each piece into a smooth round ball. Poke a hole in the middle of the ball with your index finger and stretch the hole out to 1 to 1 ½ inches. Place each bagel on the parchment. Cover with oiled plastic wrap and allow to rise for 30 minutes.
Preheat the oven to 425.
Bring the water and brown sugar to a gentle boil in a stockpot.
Mix the egg yolk and water together in a small bowl. Set aside.
Boil the bagels for two minutes, top side down. Flip and boil for one more minute. Using a strainer, remove the bagels back to the parchment.
Brush with the egg wash. Repeat until all the bagels have been boiled.
Bake the bagels for 20 minutes or until golden brown. Rotate the pans halfway through. Let the bagels cool on a wire rack for 30 minutes.
