Combine the warm water, sugar, and yeast in a large bowl or a stand mixer bowl. Let it sit for about 5 minutes to dissolve the sugar and activate the yeast.
Add 3 cups of bread flour and the salt. Switch to the dough hook attachment if you're using a stand mixer. Mix for about 8-10 minutes, adding more flour a little at a time until it forms a firm dough. If mixing by hand, knead the dough on a lightly floured surface for 8-10 minutes or until smooth.
Place the dough in a large oiled bowl and coat it with oil. Cover it loosely with a clean cloth and let it rise in a warm, draft-free place for 1-2 hours or until doubled.
As soon as the dough doubles in size, punch it down and place it on a lightly floured work surface.
Next, divide the dough into 8 pieces (for evenly sized bagels, use a kitchen scale to measure). Roll the dough pieces on the board to form a ball, then flatten them gently.
Dust your thumb or pointer finger with flour and press a hole in the middle of the ball. Then, stretch it to form a 1½-inch hole or an evenly shaped ring.
Place the bagels on a greased sheet pan. Cover with a damp cloth and let them rest for 10-12 minutes.
Preheat the oven to 425ºF (220ºC). Line a baking sheet with parchment paper and set aside.
Fill a pot about ¾ full of water and bring to a boil. Add the bagels a few at a time, being careful not to overcrowd the pot. Boil the bagels for 45 seconds, flip, and boil for another 45-60 seconds. The longer you boil the bagels, the chewier they will be.
Remove the bagels from the water with a slotted spoon and place them on a paper towel to soak up excess water. Repeat the process with the rest of the bagels. Arrange them on the prepared baking sheet.
Optional: Mix the egg, water or milk, and salt, brush it over the bagels, and sprinkle them with your desired seasoning mix or seeds to give them a beautiful, glossy crust.
Bake for 20-25 minutes or until golden brown. Remove the bagels from the baking pan and transfer them to the wire racks to cool.
Serve with cream cheese or other desired fillings.